How do you simplify #sqrt84 * sqrt28#?

Question

How do you simplify #sqrt84  * sqrt28#?

Roman Alvarez · Accepted Answer

#sqrt(84)*sqrt(28)=sqrt(28^2*3)=28sqrt(3)#

Here's a factor tree for #28#: #color(white)(0000)28# #color(white)(000)"/"color(white)(00)"\"# #color(white)(00)2color(white)(000)14# #color(white)(00000)"/"color(white)(00)"\"# #color(white)(0000)2color(white)(0000)7# So: #28 = 2^2*7# #color(white)()# Here's a factor tree for #84#: #color(white)(0000)84# #color(white)(000)"/"color(white)(00)"\"# #color(white)(00)2color(white)(000)42# #color(white)(00000)"/"color(white)(00)"\"# #color(white)(0000)2color(white)(000)21# #color(white)(0000000)"/"color(white)(00)"\"# #color(white)(000000)3color(white)(0000)7# So: #84 = 2^2*3*7 = 28*3# #color(white)()# So: #sqrt(84)*sqrt(28)=sqrt(84*28)=sqrt(28^2*3)=28sqrt(3)#

Noah Archer · Answer

undefined To simplify $ \sqrt{84} \times \sqrt{28} $, we can combine the square roots under a single radical and simplify the expression:

$$ \sqrt{84} \times \sqrt{28} = \sqrt{84 \times 28} $$

$$ = \sqrt{2352} $$

$$ = \sqrt{2 \times 1176} $$

$$ = \sqrt{2 \times 2 \times 588} $$

$$ = \sqrt{2 \times 2 \times 2 \times 294} $$

$$ = \sqrt{2 \times 2 \times 2 \times 2 \times 147} $$

$$ = \sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 49} $$

$$ = \sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 7^2} $$

$$ = \sqrt{2^4 \times 3 \times 7^2} $$

$$ = \sqrt{(2^2 \times 7)^2 \times 3} $$

$$ = (2^2 \times 7) \sqrt{3} $$

$$ = (4 \times 7) \sqrt{3} $$

$$ = 28 \sqrt{3} $$

So, $ \sqrt{84} \times \sqrt{28} $ simplifies to $ 28 \sqrt{3} $.