Question

How do you simplify \[\sqrt{49{{x}^{2}}}\]?

Answer 1

Hint: In this problem, we have to simplify the given square root. We know that to solve these types of problems, we have to know some formulas based on square root. We also know that \[{{7}^{2}}\] is 49 and we also have x square in the given expression, which is a perfect square. We can use the square root formula to solve this problem.

Complete step by step answer:
We know that the given square root expression to be solved is,
\[\sqrt{49{{x}^{2}}}\].
We know that the square root can be written as,
\[\sqrt{a}\times \sqrt{b}=\sqrt{a\times b}\]
We can apply this formula in the above given expression, we get
\[\Rightarrow \sqrt{49{{x}^{2}}}=\sqrt{49}\times \sqrt{{{x}^{2}}}\]
We also know that \[{{7}^{2}}\] is 49 and we can write it in the above step, we get
\[\Rightarrow \sqrt{49{{x}^{2}}}=\sqrt{{{7}^{2}}}\times \sqrt{{{x}^{2}}}\]
Here we can convert the square root into the fraction exponent.
We know that, to convert a square root into a fractional exponent, we have to write the \[{{n}^{th}}\] root of the base as the fractional exponent with a raised to reciprocal of that power. We can apply this in the above step, we get
\[\Rightarrow \sqrt{49{{x}^{2}}}={{7}^{2\times \frac{1}{2}}}\times {{x}^{2\times \frac{1}{2}}}\]
Now, we can cancel the similar terms, we get
\[\Rightarrow \sqrt{49{{x}^{2}}}=7x\]
Therefore, the simplified form of \[\sqrt{49{{x}^{2}}}\] is 7x.

Note:
Students make mistake while converting the square root form into a fractional exponent, we should know that to convert a square root into fractional exponent, we have to write the \[{{n}^{th}}\] root of the base as the fractional exponent with a raised to reciprocal of that power. We should also know the perfect square of some numbers to solve these types of problems.