How do you simplify #sqrt15 times sqrt21#?

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Answer 1 · 2016-08-25T10:14:03

#3sqrt35#

When multiplying 2 square roots they can be combined into one.
Write each number as the product of its prime factors.

#sqrt15 xxsqrt 21 = sqrt(5xx3xx3xx7#

=#3sqrt35#

Answer 2 · 2016-08-25T10:20:38

#3sqrt35#

When simplifying roots of natural numbers is is often useful to first express the numbers as the product of prime numbers.

Consider: #15 = 3xx5# and #21 = 3xx7#

Also: #sqrt15 xx sqrt21 = sqrt(15xx21)#

#= sqrt( 3xx5xx 3xx7)#

#=3sqrt(5xx7) = 3sqrt35#

Answer 3 · 2016-08-25T10:21:02

Same thing but with a slight twist in approach

#3sqrt(35)#

Look for common factors. Notice that 3 will divide into both 15 and 21 with no remainder.

Write as:#" "sqrt(3xx5)xxsqrt(3xx7)#

You can split these in the following way:

#sqrt(3)xxsqrt(5)xxsqrt(3)xxsqrt(7)#

But #(sqrt(3))^2=3# giving:

#3(sqrt(5)xxsqrt(7))#

But #sqrt(5)xxsqrt(7)# is the same thing as #sqrt(5xx7) =sqrt(35)#

#3sqrt(35)#