Maths-
General
Easy
Question
Find the product of 4x2 √2x5 and 5x 
. Write your answer with a perfect square factor in the radicand.
The correct answer is: Product of the given expressions with a perfect square in the radicand can be written as- √(40 × x7)2 × √3
Hint:-
A radical expression refers to an expression containing a radical (√) symbol, commonly called as a root symbol.
A radicand refers to the number that is preceded by a radical sign.
We will simplify the given expressions and find the solution with a perfect square factor in the radicand.
"Step-by-step solution:-
Product of given Expression = 4x2 √2x5 × 5x √6x3
∴ Product of given Expression = √16x4 × √2x5 ×√25x2 × √6x3
∴ Product of given Expression = √(16x4 × √2x5 × √25x2 × √6x3) …................................ (Product property)
∴ Product of given Expression = √(16 × 2 × 25 × 6 × x4 × x5 × x2 × x3)
∴ Product of given Expression = √(4,800 × x4+5+2+3) ........................................................ (am × an = am + n)
∴ Product of given Expression = √(4,800 × x14)
∴ Product of given Expression = √(1,600 × 3 ×x14) ......................................................... (Factorizing 4,800)
∴ Product of given Expression = √(1,600 × x14) × √3 ....................................................... (Product property)
∴ Product of given Expression = √(1,600 × x7×2) × √3
∴ Product of given Expression = √(40)2 × (x7)2 × √3 ........................................................ [am×n = (am)n]
∴ Product of given Expression = √(40 × x7)2 × √3 ............................................................ (am × bm = abm)
Final Answer:-
∴ Product of the given expressions with a perfect square in the radicand can be written as- √(40 × x7)2 × √3.
Note:-
Alternatively, if the questioned had asked for the product without a perfect square in the radicand, the answer would be written as-
40x7 × √3.
Final answer remains the same.
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A. The cost of 4 tetras is the same as the cost of a rainbow fish.
B. One rainbow fish plus 5 tetras Cost $21.
C. An equation to find the cost r, in dollars of a rainbow fish is 8r + 2(r + 6) = 37
D. Reducing the number of rainbow fish by 1 would result in a total cost of $28.50
E. An equation to find the cost t, in dollars , of a tetra is 8t + 2t + 6 = 37
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