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How do you simplify #sqrt150 + sqrt 40#?

Answer 1

#5sqrt(6)+2sqrt(10)#

#sqrt(150)+sqrt(40)# #sqrt(25*6)+sqrt(40)# #color(blue)("Find a factor of 150 that is also a perfect square")# #5sqrt(6)+sqrt(40)# #color(blue)("Since 25 is a perfect square, pull out a 5")# #5sqrt(6)+sqrt(10*4)# #color(blue)("Find a factor of 40 that is also a perfect square")# #5sqrt(6)+2sqrt(10)# #color(blue)("Since 4 is a perfect square, pull out a 2")#

A perfect square is a number that can be pulled out of a radical by multiplying a constant together twice #(5*5=25)#.

#sqrt(6)# and #sqrt(10)# can't be simplified since there are no factors of 6 or 10 that are perfect squares.

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Answer 2

Ethan Adkins

To simplify √150 + √40, we can break down the square roots into their simplest forms and then combine like terms.

First, we find the prime factorization of 150 and 40: 150 = 2 × 3 × 5^2 40 = 2^3 × 5

Next, we simplify the square roots: √150 = √(2 × 3 × 5^2) = 5√6 √40 = √(2^3 × 5) = 2√10

Finally, we combine the like terms: 5√6 + 2√10 is the simplified form of √150 + √40.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.