Question

How do you solve \[{{x}^{2}}=29\]?

Answer 1

Hint: In this problem, we have to solve the given expression. We can take the square root on both the left-hand side and the right-hand side. We know that, after taking the square root on both sides, on the left-hand side we can convert the square root to fractional exponent and we can cancel the square of x and fractional exponent to get the value of x.

Complete step-by-step solution:
We know that the given expression to be solved is,
\[{{x}^{2}}=29\]
We can now take square root on the both left-hand side and the right-hand side, we get
\[\Rightarrow \sqrt{{{x}^{2}}}=\pm \sqrt{29}\]
On the left-hand side we can convert the square root to fractional exponent and we can cancel the square of x and fractional exponent to get the value of x.
We can now write the left-hand side of the above expression as,
\[\Rightarrow {{x}^{2\times \dfrac{1}{2}}}=\pm \sqrt{29}\] .
Now we can cancel the similar terms in the left-hand side of the above expression, we get
\[\Rightarrow x=\pm \sqrt{29}\]
We can see that, in the above solution 29 is not a perfect square, so we can either use a long division method or use a calculator to find the value of root 29.
Therefore, the value of \[x=\pm \sqrt{29}=\pm 5.358\].

Note: Students make mistakes while taking square roots and finding the exact value. We should know whether the number inside the square root is a perfect square or not, if not we can use a calculator to find the value of x. Students may forget the symbol plus or minus, before the square root which should be concentrated.