How do you simplify #(7-sqrt7)/(10+sqrt3)#?

Answer 1

See below

Given expression ,

#(7-sqrt7)/(10+sqrt3)#

We get,

# (7-sqrt7)/(10+sqrt3) * (10-sqrt3)/(10-sqrt3) =# # ((7-sqrt7)*(10-sqrt3))/(10^2-(sqrt3)^2)=# # (70-7sqrt3-10sqrt7+sqrt21)/97#

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Answer 2

Jameson Allen

To simplify the expression (7 - √7)/(10 + √3), we need to rationalize the denominator. Multiply both the numerator and denominator by the conjugate of the denominator, which is (10 - √3).

[(7 - √7)/(10 + √3)] * [(10 - √3)/(10 - √3)]

Simplifying the numerator and denominator:

[(7 * 10) - (7 * √3) - (√7 * 10) + (√7 * √3)] / [(10 * 10) - (10 * √3) + (√3 * 10) - (√3 * √3)]

[70 - 7√3 - 10√7 + √21] / [100 - √30 + √30 - 3]

Combine like terms:

[70 - 10√7 - 7√3 + √21] / [100 - 3]

Simplify further:

[70 - 10√7 - 7√3 + √21] / 97

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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.