What value of y will make the equation true?

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asked Mar 27, 2022 86.0k views

1 Answer

Tharindu Vindula · Answer 1 · 2022-04-02T09:44:41+0000

Generally the value of y would be 34 because same two square roots of n multiplying each others would equal to n by the definition.

$\large \boxed{ √(a) * √(a) = ( √(a) )^(2) = a}$

Although it is easy to predict the solution of y-value, I will be showing you how to solve the radical equation for y-term which will be useful.

$\large \boxed{ √(a) * √(b) = √(ab) }$

So from the equation, convert √34 × √y to √34y

$\large{ √(34) * √(y) = 34} \\ \large{ √(34y) = 34}$

Then we square both sides to get rid of the square root.

$\large{ {( √(34y) )}^(2) = {34}^(2) } \\ \large{34y = 1156}$

Divide both sides by 34 so we can finally isolate the y-term.

$\large{ (34y)/(34) = (1156)/(34) } \\ \large \boxed{y = 34}$

Hence the value of y is 34.

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