Question

What value of y will make the equation true?

Answer 1

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.

$\large \boxed{ \sqrt{a} \times \sqrt{a} = ( \sqrt{a} )^{2} = a}$

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.

$\large \boxed{ \sqrt{a} \times \sqrt{b} = \sqrt{ab} }$

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

$\large{ \sqrt{34} \times \sqrt{y} = 34} \\ \large{ \sqrt{34y} = 34}$

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

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

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

$\large{ \frac{34y}{34} = \frac{1156}{34} } \\ \large \boxed{y = 34}$

Hence the value of y is 34.

Answer

• y = 34