How do you solve $36{{w}^{2}}=121$ ?

Hint: We know that the value of $36{{w}^{2}}$ is equal to 121, so we can find the value of square of w by dividing 121 by 36. The quotient may be a fraction. The value of w will be the square root of the quotient. We know that $\sqrt{\dfrac{a}{b}}$ is equal to $\dfrac{\sqrt{a}}{\sqrt{b}}$ where b is not equal to 0.

Complete step by step answer:
We have to solve $36{{w}^{2}}=121$ , by dividing by 36 both side we get ${{w}^{2}}$ is equal to $\dfrac{121}{36}$ .
So the value of w is equal to the square root of $\dfrac{121}{36}$ . We know that $\sqrt{\dfrac{a}{b}}$ is equal to $\dfrac{\sqrt{a}}{\sqrt{b}}$ where b is not equal to 0.
So the value of $\sqrt{\dfrac{121}{36}}$ is equal to $\dfrac{\sqrt{121}}{\sqrt{36}}$ . square root of 121 is equal to 11 and square root of 36 is equal to 6
So we can write $\sqrt{\dfrac{121}{36}}$ is equal to $\dfrac{11}{6}$ . w = $\dfrac{11}{6}$ is the solution of $36{{w}^{2}}=121$

Note:
There will be no solution for the equation $a{{x}^{2}}=b$ if a and b have opposite sign that means if there will be exist a real solution for the equation $a{{x}^{2}}=b$ if a is positive and b is non negative and if a is negative and b is less than equal to 0. The value of a can not be 0 if b is not equal to 0. Always remember $\sqrt{\dfrac{a}{b}}$ is equal to $\dfrac{\sqrt{a}}{\sqrt{b}}$ when b is not equal to 0. We can not make the denominator 0.