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How do you simplify #sqrt 5(sqrt 2+sqrt 10)#?

Answer 1

#sqrt(10)(1+sqrt(5))# or #sqrt(2)(sqrt(5)+5)#

#sqrt(5)(sqrt(2)+sqrt(10))# #=sqrt(5)*sqrt(2)+sqrt(5)*sqrt(10)# #=sqrt(5*2)+sqrt(5)*sqrt(10)# #=sqrt(10)+sqrt(5)*sqrt(10)# #=sqrt(10)(1+sqrt(5))#

#sqrt(5)(sqrt(2)+sqrt(10))# #=sqrt(5)*sqrt(2)+sqrt(5)*sqrt(10)# #=sqrt(5)*sqrt(2)+sqrt(5*10)# #=sqrt(5)*sqrt(2)+sqrt(50)# #=sqrt(5)*sqrt(2)+sqrt(2*25)# #=sqrt(5)*sqrt(2)+sqrt(2)*sqrt(25)# #=sqrt(5)*sqrt(2)+5sqrt(2)# #=sqrt(2)(sqrt(5)+5)#

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Answer 2

Hazel Anglin

To simplify the expression sqrt 5(sqrt 2+sqrt 10), you can distribute the square root of 5 to both terms inside the parentheses. This gives you sqrt 5 * sqrt 2 + sqrt 5 * sqrt 10. Simplifying further, you can multiply the square roots together, resulting in sqrt (5 * 2) + sqrt (5 * 10). This simplifies to sqrt 10 + sqrt 50. Finally, you can simplify the square root of 50 by factoring out the largest perfect square, which is 25. This gives you sqrt 10 + 5sqrt 2 as the simplified form of sqrt 5(sqrt 2+sqrt 10).

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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.