Mathematics: Which expression is equal to 2√28 + 2√63? a: 13√7 b: 4√7 c: 10√7 d: 12√7

idkStep-by-step explanation:...

Which expression is equal to 2√28 + 2√63? a: 13√7

bree480

01.01.2022

Step-by-step explanation:

Using the rule of radicals

$\sqrt{a}$ × $\sqrt{b}$ ⇔ $\sqrt{ab}$

Simplifying the radicals

$\sqrt{28}$

= $\sqrt{4(7)}$

= $\sqrt{4}$ × $\sqrt{7}$ = 2 $\sqrt{7}$

and

$\sqrt{63}$

= $\sqrt{9(7)}$

= $\sqrt{9}$ × $\sqrt{7}$ = 3 $\sqrt{7}$

Hence

2 $\sqrt{28}$ + 2 $\sqrt{63}$

= 2(2 $\sqrt{7}$ ) + 2(3 $\sqrt{7}$ )

= 4 $\sqrt{7}$ + 6 $\sqrt{7}$

= 10 $\sqrt{7}$ → C

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