Maths-
General
Easy

Question

Find the values of a and b : fraction numerator 5 plus 3 square root of 2 over denominator 5 minus 3 square root of 2 end fraction equals a plus b square root of 2

hintHint:

Hint:
Rationalization is a technique which is used to eliminate the irrational number in the denominator. For example,fraction numerator 1 over denominator square root of 3 end fraction
can be rationalised as fraction numerator 1 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction equals fraction numerator square root of 3 over denominator 3 end fraction

The correct answer is: Values of a and b 43/7 and 30/7


    Step 1 of 2:
    Let’s say x =fraction numerator 5 plus 3 square root of 2 over denominator 5 minus 3 square root of 2 end fraction
    To rationalise the denominator, we can multiply 5 plus 3 square root of 2   to the numerator and denominator.
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals fraction numerator 5 plus 3 square root of 2 over denominator 5 minus 3 square root of 2 end fraction cross times fraction numerator 5 plus 3 square root of 2 over denominator 5 plus 3 square root of 2 end fraction end cell row cell x equals fraction numerator left parenthesis 5 plus 3 square root of 2 right parenthesis squared over denominator 5 squared minus left parenthesis 3 square root of 2 right parenthesis squared end fraction end cell row cell x equals fraction numerator 25 plus 18 plus 2 cross times 5 cross times 3 square root of 2 over denominator 25 minus 18 end fraction end cell row cell x equals fraction numerator 25 plus 18 plus 2 cross times 5 cross times 3 square root of 2 over denominator 7 end fraction end cell row cell x equals fraction numerator 43 plus 30 square root of 2 over denominator 7 end fraction end cell row cell x equals 43 over 7 plus 30 over 7 square root of 2 end cell end table
    Step 2 of 2:
    Now,        table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a plus b square root of 2 equals 43 over 7 plus 30 over 7 square root of 2 end cell row cell a equals 43 over 7 comma b equals 30 over 7 end cell end table
    Step 2 of 2:
    Now,    table attributes columnspacing 1em end attributes row cell a plus b square root of 2 equals 43 over 7 plus 30 over 7 square root of 2 end cell row cell straight a equals 43 over 7 comma straight b equals 30 over 7 end cell end table
    Final Answer:
    Hence, the value of a is 43 over 7 and b is .30 over 7

    Related Questions to study

    General
    Maths-

    if fraction numerator 4 plus square root of 5 over denominator 4 minus square root of 5 end fraction plus fraction numerator 4 minus square root of 5 over denominator 4 plus square root of 5 end fraction equals a plus b square root of 5. Then, find the values of a and b.

    if fraction numerator 4 plus square root of 5 over denominator 4 minus square root of 5 end fraction plus fraction numerator 4 minus square root of 5 over denominator 4 plus square root of 5 end fraction equals a plus b square root of 5. Then, find the values of a and b.

    Maths-General
    General
    Maths-

    A rainfall of 0.896 cm was recorded in 7 hours. What was the average amount of rainfall per hour?

    A rainfall of 0.896 cm was recorded in 7 hours. What was the average amount of rainfall per hour?

    Maths-General
    General
    Maths-

    Three bricklayers, Maric, Hugh and Ethan, are cladding a new home. If Maric were to work alone, the job would take him 8 days to complete. If Hugh were to work alone, the job would take him 6 days to complete and if Ethan were to work by himself, the job would take him 12 days to complete. a) If the three men work together, how long will it take them to complete the job? b) What fraction of the house will each bricklayer complete?

    Three bricklayers, Maric, Hugh and Ethan, are cladding a new home. If Maric were to work alone, the job would take him 8 days to complete. If Hugh were to work alone, the job would take him 6 days to complete and if Ethan were to work by himself, the job would take him 12 days to complete. a) If the three men work together, how long will it take them to complete the job? b) What fraction of the house will each bricklayer complete?

    Maths-General
    parallel
    General
    Maths-

    A can do a piece of work in 40 days and B in 45 days. They work together for 10 days and then B goes away. In how many days will A finish the remaining work?

    A can do a piece of work in 40 days and B in 45 days. They work together for 10 days and then B goes away. In how many days will A finish the remaining work?

    Maths-General
    General
    Maths-

    A and B can do a piece of work in 20 days and B in 15 days. They work together for 2 days and then A goes away. In how many days will B finish the remaining work?

    A and B can do a piece of work in 20 days and B in 15 days. They work together for 2 days and then A goes away. In how many days will B finish the remaining work?

    Maths-General
    General
    Maths-

    Simplifyfraction numerator 1 over denominator 2 plus square root of 5 end fraction plus fraction numerator 1 over denominator square root of 5 plus square root of 6 end fraction plus fraction numerator 1 over denominator square root of 6 plus square root of 7 end fraction plus fraction numerator 1 over denominator square root of 7 plus square root of 8 end fraction

    Simplifyfraction numerator 1 over denominator 2 plus square root of 5 end fraction plus fraction numerator 1 over denominator square root of 5 plus square root of 6 end fraction plus fraction numerator 1 over denominator square root of 6 plus square root of 7 end fraction plus fraction numerator 1 over denominator square root of 7 plus square root of 8 end fraction

    Maths-General
    parallel
    General
    Maths-

    A and B can finish a work in 20 days. A alone can do 1/5th of the work in 12 days. In how many days can B alone do it?

    A and B can finish a work in 20 days. A alone can do 1/5th of the work in 12 days. In how many days can B alone do it?

    Maths-General
    General
    Maths-

    8 bags of cattle feed are needed to feed 4 cows for 2 months. How long will the same feed last to feed 6 cows?

    8 bags of cattle feed are needed to feed 4 cows for 2 months. How long will the same feed last to feed 6 cows?

    Maths-General
    General
    Maths-

    A and B can polish the floors of a building in 10 days. A alone can do ¼th of it in 12 days. In how many days can B alone polish the floor?

    A and B can polish the floors of a building in 10 days. A alone can do ¼th of it in 12 days. In how many days can B alone polish the floor?

    Maths-General
    parallel
    General
    Maths-

    A, B and C can reap a field in 15 ¾ days; B, C and D in 14 days; C, D and A in 18 days; D, A and B in 21 days. In what time can A, B, C and D together reap it?

    A, B and C can reap a field in 15 ¾ days; B, C and D in 14 days; C, D and A in 18 days; D, A and B in 21 days. In what time can A, B, C and D together reap it?

    Maths-General
    General
    Maths-

    A rope makes 260 rounds of a cylinder with a base radius 20 cm. How many times can it go round a cylinder with a base radius 26cm?

    A rope makes 260 rounds of a cylinder with a base radius 20 cm. How many times can it go round a cylinder with a base radius 26cm?

    Maths-General
    General
    Maths-

    A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. How much time will A alone take to finish the work?

    A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. How much time will A alone take to finish the work?

    Maths-General
    parallel
    General
    Maths-

    A and B can do a piece of work in 18 days; B and C in 24 days and A and C in 36 days. In what time can they do it, all working together?

    A and B can do a piece of work in 18 days; B and C in 24 days and A and C in 36 days. In what time can they do it, all working together?

    Maths-General
    General
    Maths-

    A, B and C working together can do a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?

    A, B and C working together can do a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?

    Maths-General
    General
    Maths-

    If x equals 2 plus square root of 3 find the values of x squared plus 1 over x squared

    If x equals 2 plus square root of 3 find the values of x squared plus 1 over x squared

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.