√6(√10 + √15) simplify show all work

2 sqrt(15) + 3 sqrt(10)

Step-by-step explanation:

sqrt(6) * ( sqrt(10)+ sqrt(15))

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We know that sqrt(a) sqrt(b) = sqrt(ab)

sqrt(6) sqrt(10)+  sqrt(6) sqrt(15))

sqrt(60) + sqrt( 90)

sqrt( 4*15) + sqrt(9*10)

We know that sqrt(a) sqrt(b) = sqrt(ab)

sqrt(4) sqrt(15) + sqrt(9) sqrt(10)

2 sqrt(15) + 3 sqrt(10)

≈ 15.5085

Step-by-step explanation:

√6 ≈ 2.45

6 is not a perfect square so its square root is irrational, therefore the decimal form can only be estimated.

√10 ≈ 3.16

The square root of 10 is a single number. That number is irrational, which means that its decimal expansion goes on forever without repeating, and cannot be expressed as a fraction.

√15 ≈ 3.17

This is not simplifiable. But this is approximately what equalled.

2.45(3.16 + 3.17)

= 15.5085

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