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Simplify the following expressions: d) (sqrt(5)+2)(sqrt(5)-1) h) 7sqrt(30) / sqrt(2)

April 22, 2026Mathematics

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2 parts

3 + \sqrt{5}

7\sqrt{15}

6 steps

Here are the simplifications for the expressions:

Use the FOIL method to expand the product of the two binomials.
$(\sqrt{5}+2)(\sqrt{5}-1) = \sqrt{5} \times \sqrt{5} + \sqrt{5} \times (-1) + 2 \times \sqrt{5} + 2 \times (-1)$
Simplify each term.
$5 - \sqrt{5} + 2\sqrt{5} - 2$
Combine like terms.
$(5-2) + (-1+2)\sqrt{5}$ $3 + \sqrt{5}$ $\boxed{3 + \sqrt{5}}$

Rewrite the division as a fraction.
$7\sqrt{30} \div \sqrt{2} = \frac{7\sqrt{30}}{\sqrt{2}}$
Separate the coefficient and the surds.
$7 \times \frac{\sqrt{30}}{\sqrt{2}}$
Simplify the surds.
$7 \times \sqrt{\frac{30}{2}}$ $7 \times \sqrt{15}$ $7\sqrt{15}$ $\boxed{7\sqrt{15}}$

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