Question

rationalize the denominator 7/ root 15 + 2 root 2
answer in full

Answer 1

7 / (√15 + 2√2)

7 (√15 - 2√2) / (√15 + 2√2)(√15 - 2√2)

7 (√15 - 2√2)/ (√15)² - (2√2)²

7(√15 - 2√2) / (15 - 8)

7 (√15 - 2√2) / 7

= √15 - 2√2

Answer 2

The rationalized form of the given expression is (√15)/7 - 14√2.

Rationalization:

• To make it simpler to execute any calculations on the rational number, we rationalize the denominator.
• When we rationalize the denominator of a fraction, we are removing any radical expressions from the denominator, such as square roots and cube roots.
• An expression is rationalized by multiplying it by another expression that is similar in order to produce a rational number.
• The rationalization factor (RF) is the expression that is multiplied.

Here are the steps to rationalize the given number:

$\frac{7}{\sqrt{15}+2\sqrt{2}}\\\\= \frac{7(\sqrt{15}-2\sqrt{2})}{(\sqrt{15}+2\sqrt{2})(\sqrt{15}-2\sqrt{2})}\\\\= \frac{7(\sqrt{15}-2\sqrt{2})}{15 -2\sqrt{30}+2\sqrt{30}-8}\\\\= \frac{\sqrt{15}-14\sqrt{2}}{7}\\\\= \frac{\sqrt{15}}{7}- 2\sqrt{2}}$

Therefore, the rationalized form of the given expression is (√15)/7 - 14√2.

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