Question

Simplify (√5 − √2 )(√5 + √2)

Answer 1

(√5 − √2)(√5 + √2) = 3

We know that (a + b) (a - b) = a² - b²

= (√5 + √2) (√5 − √2)

= (√5)² - (√2)²

= 5 - 2

= 3

Answer 2

(√5 − √2)(√5 + √2) = 3

Explanation:

To simplify (√5 − √2)(√5 + √2) use the FOIL method.

What is the FOIL method?

FOIL is an acronym that refers to the order of multiplying the terms inside the parentheses of two binomials. Multiply the First terms, then the Outside terms, then Inside terms, then Last terms.

Therefore:

`\begin{aligned}(√(5)-√(2))(√(5)+√(2))&=√(5)√(5)+√(5)√(2)-√(2)√(5)-√(2)√(2)\\&=5+√(5)√(2)-√(5)√(2)-2\\&=5-2\\&=3\end{aligned}`