Question

# To simplify the expression, \sqrt{23}.

Factors and multiples
To simplify the expression, $$\displaystyle\sqrt{{{23}}}$$.

2021-08-07
Concept used:
To simplify an expression having square root of a number, firstly factorization of the number is done and then factors having even exponential powers are taken out from the square root function and their exponential powers are divided by two.
$$\displaystyle\Rightarrow\sqrt{{{m}^{{{4}}}\times{n}^{{{2}}}}}={m}^{{{\frac{{{4}}}{{{2}}}}}}\times{n}^{{{\frac{{{2}}}{{{2}}}}}}={m}^{{{2}}}\times{n}^{{{1}}}$$
Calculations:
As per the question, the expression is $$\displaystyle\sqrt{{{23}}}$$.
The factorization of a number is the product of numbers that equals the number.
Now, 23 is a prime number. Hence, it has only two multiples i.e. 1 and 23.
Therefore, 12 cannot be factorized anymore.
Hence, the simplified value of $$\displaystyle\sqrt{{{23}}}$$ is $$\displaystyle\sqrt{{{23}}}$$ only.