# Simplifying Square Root: With a number and variable

I am currently doing a math problem, and was confused about whether I was allowed to further simplify √x∗√35\sqrt x * \sqrt{35} into √35x\sqrt{35x}

I have searched online and could not find any sources which stated it would be okay to do.

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Yes, it is ok…
– imranfat
Oct 20 at 20:05

Square root is “a power” not integer but fractional and you have the algebraic elementary formula am⋅bm=(ab)ma^m\cdot b^m=(ab)^m You have just applied this.
– Piquito
Oct 20 at 20:43

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2

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am⋅bm=(ab)ma^m \cdot b^m = (ab)^m

E.g.,

91/2⋅161/2=3⋅4=(9⋅16)1/2=1441/2=129^{1/2} \cdot 16^{1/2} = 3 \cdot 4 = (9 \cdot 16)^{1/2} = 144^{1/2} = 12

Would you mind using proper math formatting ?
– imranfat
Oct 20 at 20:32

You can simplify an expression under a radical by extracting perfect squares. For example, √24=√4⋅6=√4⋅√6=2⋅√6=2√6.\sqrt{24}=\sqrt{4\cdot6}=\sqrt{4}\cdot\sqrt{6}=2\cdot\sqrt{6}=2\sqrt{6}. What you are proposing is doing the opposite, i.e. turning 2√62\sqrt{6} into √24\sqrt{24}. Since one direction is allowed, what you are proposing is also perfectly “legal.”