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Maths-

General

Easy

Question

Arrange in ascending order of magnitude :
$square root of 5 comma space cube root of 11 comma 2 times root index 6 of 3$

The correct answer is: Use LCM property

Complete step by step solution:
Here we can write, $square root of 5 equals 5 to the power of 1 half end exponent comma cube root of 11 equals 11 to the power of 1 third end exponent$ and $2 root index 6 of 3 equals root index 6 of 12 equals 12 to the power of 1 over 6 end exponent$
On taking the LCM of 2,3,6 we have LCM as 6.
So, $not stretchy rightwards double arrow 5 to the power of 1 half end exponent equals 5 to the power of fraction numerator 1 cross times 3 over denominator 2 cross times 3 end fraction end exponent equals 5 to the power of 3 over 6 end exponent$
$not stretchy rightwards double arrow open parentheses 5 cubed close parentheses to the power of 1 over 6 end exponent equals 125 to the power of 1 over 6 end exponent open parentheses Since subscript midline horizontal ellipsis invisible function application open parentheses a to the power of b close parentheses to the power of c equals a to the power of b c end exponent close parentheses$
Likewise, $not stretchy rightwards double arrow 11 to the power of 1 third end exponent equals 11 to the power of fraction numerator 1 cross times 2 over denominator 3 cross times 2 end fraction end exponent equals 11 to the power of 2 over 6 end exponent$
$not stretchy rightwards double arrow open parentheses 11 squared close parentheses to the power of 1 over 6 end exponent equals 121 to the power of 1 over 6 end exponent space of 1em open parentheses text Since end text open parentheses a to the power of b close parentheses to the power of c equals a to the power of b c end exponent close parentheses$
Likewise, = $12 to the power of 1 over 6 end exponent$
Now, we have , $125 to the power of 1 over 6 end exponent comma space 121 to the power of 1 over 6 end exponent$ and $12 to the power of 1 over 6 end exponent$
So, here ascending order is $12 less than 121 less than 125$
$not stretchy rightwards double arrow 12 to the power of 1 over 6 end exponent less than 121 to the power of 1 over 6 end exponent less than 125 to the power of 1 over 6 end exponent$
$not stretchy rightwards double arrow 12 to the power of 1 over 6 end exponent less than 11 to the power of 1 third end exponent less than 5 to the power of 1 half end exponent$
$not stretchy rightwards double arrow root index 6 of 12 less than cube root of 11 less than root index blank of 5$

Related Questions to study

Which is greater ?
$root index 6 of 3 comma space fourth root of 5 comma space square root of 2$

Which is greater ?
$root index 6 of 3 comma space fourth root of 5 comma space square root of 2$

Arrange the following from least to greatest :
0.1666666666...... , 1.66666666666.......... , 1.388888888888...............

Arrange the following from least to greatest :
0.1666666666...... , 1.66666666666.......... , 1.388888888888...............

Simplify $4 over 7 plus fraction numerator negative 8 over denominator 9 end fraction plus fraction numerator negative 5 over denominator 21 end fraction plus 1 third$

Simplify $4 over 7 plus fraction numerator negative 8 over denominator 9 end fraction plus fraction numerator negative 5 over denominator 21 end fraction plus 1 third$

parallel

The sum of two rational numbers is -8. If one of them is - $13 over 6$ , find the other ?

The sum of two rational numbers is -8. If one of them is - $13 over 6$ , find the other ?

Arrange from greatest to least ?
$fraction numerator negative 10 over denominator 11 end fraction comma fraction numerator 19 over denominator negative 22 end fraction comma fraction numerator negative 23 over denominator 33 end fraction comma fraction numerator negative 39 over denominator 44 end fraction$

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Arrange from least to greatest : $fraction numerator 3 over denominator negative 5 end fraction comma fraction numerator negative 7 over denominator 10 end fraction comma fraction numerator negative 11 over denominator 15 end fraction comma fraction numerator negative 13 over denominator 20 end fraction$

Arrange from least to greatest : $fraction numerator 3 over denominator negative 5 end fraction comma fraction numerator negative 7 over denominator 10 end fraction comma fraction numerator negative 11 over denominator 15 end fraction comma fraction numerator negative 13 over denominator 20 end fraction$

parallel

An orange crate is in the shape of a rectangular prism . It has a volume of $3 x cubed plus 7 x squared plus 2 x$ cubic units and has a base area of $x squared plus 2 x$ square units. Find the height of the orange crate ?.

An orange crate is in the shape of a rectangular prism . It has a volume of $3 x cubed plus 7 x squared plus 2 x$ cubic units and has a base area of $x squared plus 2 x$ square units. Find the height of the orange crate ?.

Arrange the following rational numbers in descending order: $fraction numerator negative 4 over denominator 9 end fraction comma fraction numerator negative 5 over denominator 12 end fraction comma fraction numerator negative 7 over denominator 18 end fraction comma fraction numerator negative 2 over denominator 3 end fraction$

Arrange the following rational numbers in descending order: $fraction numerator negative 4 over denominator 9 end fraction comma fraction numerator negative 5 over denominator 12 end fraction comma fraction numerator negative 7 over denominator 18 end fraction comma fraction numerator negative 2 over denominator 3 end fraction$

Arrange from least to greatest : $fraction numerator negative 3 over denominator 5 end fraction comma space fraction numerator negative 7 over denominator 10 end fraction comma space fraction numerator negative 5 over denominator 8 end fraction$

Arrange from least to greatest : $fraction numerator negative 3 over denominator 5 end fraction comma space fraction numerator negative 7 over denominator 10 end fraction comma space fraction numerator negative 5 over denominator 8 end fraction$

parallel

The product of two rational numbers is $13 over 5$ . If one of the number is $fraction numerator negative 3 over denominator 4 end fraction$ , find the other rational number ?

The product of two rational numbers is $13 over 5$ . If one of the number is $fraction numerator negative 3 over denominator 4 end fraction$ , find the other rational number ?

Find the Quotient and the domain .
$fraction numerator straight x to the power of 4 plus straight x cubed minus 30 straight x squared over denominator straight x squared minus 3 straight x minus 18 end fraction divided by fraction numerator straight x cubed plus straight x squared minus 30 straight x over denominator straight x squared minus 36 end fraction$

Find the Quotient and the domain .
$fraction numerator straight x to the power of 4 plus straight x cubed minus 30 straight x squared over denominator straight x squared minus 3 straight x minus 18 end fraction divided by fraction numerator straight x cubed plus straight x squared minus 30 straight x over denominator straight x squared minus 36 end fraction$

What is the Quotient of $fraction numerator x squared plus x minus 2 over denominator x plus 3 end fraction straight & fraction numerator x squared plus 3 x minus 4 over denominator 2 x plus 6 end fraction$ .

What is the Quotient of $fraction numerator x squared plus x minus 2 over denominator x plus 3 end fraction straight & fraction numerator x squared plus 3 x minus 4 over denominator 2 x plus 6 end fraction$ .

parallel

The cost of 4.25 m of cloth is 38.25. Find the cost of cloth per meter ?

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Taylor uses tape to mark a square play area in the basement for her daughter. The area measures 28 sq.ft . Is the side length of the square rational or irrational ? Explain.

Taylor uses tape to mark a square play area in the basement for her daughter. The area measures 28 sq.ft . Is the side length of the square rational or irrational ? Explain.

parallel

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