# What is the square root of 625 simplified in radical form?

Apr 24, 2017

25

#### Explanation:

$\sqrt{625} = \sqrt{25 \cdot 25} = \sqrt{{25}^{2}} = 25$

Also, let's not forget that -25 works too!

$\sqrt{625} = \pm 25$

Apr 24, 2017

$\sqrt{625} = \pm 25$

If no calculator to hand it is always worth trying this type of trick

#### Explanation:

Consider the last digit of 625

This is 5. So the first question is, what times itself give the last digit of 5.

Known that $5 \times 5 = 25$ giving us the last digit so 5 is a $\underline{\text{potential}}$ part of the solution

Consider the hundreds ie 600

$10 \times 10 = 100 < 600$
$20 \times 20 = 2 \times 200 = 400 < 600$
$30 \times 30 = 3 \times 300 = 900 > 600 \textcolor{red}{\text{ Fail as too large}}$

Putting this together lets test $25 \times 25$

$= \left(20 + 5\right) \times 25 = 500 + 125 = 625$ as required

However: $\textcolor{g r e e n}{\left(+ 25\right) \times \left(+ 25\right)} \textcolor{b l u e}{= \left(- 25\right) \times \left(- 25\right)} \textcolor{m a \ge n t a}{= + 625}$

So $\sqrt{625} = \pm 25$
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$\textcolor{b l u e}{\text{Additional comment}}$

If all else fails and you do not have a calculator to hand build a prime factor tree. From this observe that we have ${5}^{2} \times {5}^{2} \to 25 \times 25$

So $\sqrt{625} \to \sqrt{{25}^{2}} = \pm 25$