Question

To simplify the expression, \sqrt{23}.

Factors and multiples
ANSWERED
asked 2021-08-06
To simplify the expression, \(\displaystyle\sqrt{{{23}}}\).

Answers (1)

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.
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