Rationalizing Denominators Warmup 2

Answer explanation

To simplify \( \frac{8\sqrt{7}}{\sqrt{10}} \), multiply numerator and denominator by \( \sqrt{10} \): \( \frac{8\sqrt{70}}{10} = \frac{4\sqrt{70}}{5} \). Thus, the correct answer is \( \frac{4\sqrt{70}}{5} \).

Answer explanation

To rationalize the denominator of \( \frac{\sqrt{5}}{2\sqrt{3}} \), multiply the numerator and denominator by \( \sqrt{3} \): \( \frac{\sqrt{15}}{6} \). Thus, the correct answer is \( \frac{\sqrt{15}}{6} \).

Tags

CCSS.HSN.RN.A.2

• 14

• 18

Answer explanation

To multiply (4+√2)(4-√2), use the difference of squares formula: a^2 - b^2. Here, a=4 and b=√2. Thus, (4)^2 - (√2)^2 = 16 - 2 = 14. The correct answer is 14.

Tags

CCSS.HSN.RN.A.2

• -4

Answer explanation

To rationalize the denominator of \( \frac{6}{1-\sqrt{5}} \), multiply by the conjugate \( 1+\sqrt{5} \). This eliminates the square root in the denominator, making it a rational number.

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