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Rationalising the Denominator - Questions

Question 1
14621

By rationalising the denominator, which surd is equivalent to \(\dfrac{{15}}{{\sqrt 6 }}\)

A.

\(\dfrac{3}{2}\;\sqrt 6 \)

B.

\(\dfrac{5}{2}\;\sqrt 6 \)

C.

\(3\;\sqrt 6 \)

D.

\(5\sqrt 6 \)

\(\dfrac{5}{2}\;\sqrt 6 \)

Question 2
14622

By rationalising the denominator, which surd is equivalent to \(\dfrac{{8\sqrt 3 }}{{5\sqrt 7 }}\)

A.

\(\dfrac{8}{{35}}\;\sqrt {21} \)

B.

\(\dfrac{8}{{15}}\;\sqrt {21} \)

C.

\(\dfrac{{24}}{{35}}\;\sqrt 7 \)

D.

\(\dfrac{{24}}{5}\;\sqrt {21} \)

\(\dfrac{8}{{35}}\;\sqrt {21} \)

Question 3
14626

If \(\dfrac{4}{{\sqrt {15} }} + \dfrac{5}{{\sqrt 6 }}\) is simplified with a rational denominator, the numerator of this expression is ?

\(8\sqrt {15} + 25\sqrt 6 \)

Question 4
12715

\(\dfrac{{10}}{{5\sqrt 2 }}=\) 

\(\sqrt 2 \)

Question 5
12717

Simplify \(4\sqrt 3 - \dfrac{3}{{\sqrt {27} }} - \sqrt {243} \)

\( - \dfrac{{16}}{3}\sqrt 3 \)

Question 6
14628

If \(\dfrac{{5 + \sqrt 6 }}{{5 - \sqrt 6 }}\) is simplified with a rational denominator, the numerator of this expression is

\(31 + 10\sqrt 6 \)

Question 7
14632

If \(\dfrac{{\sqrt 6 + \sqrt 2 }}{{\sqrt 5 + \sqrt 3 }}\) is simplified with a rational denominator, the numerator of this expression is

\(\sqrt {30} + \sqrt {10} - 3\sqrt 2 - \sqrt 6 \)

Question 8
112209

Write \(\dfrac{4}{\sqrt{2}}\) in the form \(a\sqrt{b}\)

\(2\sqrt{2}\)

Question 9
112210

Write \(\dfrac{2\sqrt{45}}{3\sqrt{2}}\) in the form \(a\sqrt{b}\)

\(\sqrt{10}\)

Question 10
112211

Write \(\dfrac{3}{\sqrt{2}-\sqrt{3}}\) in the form \(a(\sqrt{b}+\sqrt{c})\)

\(-3(\sqrt{2}+\sqrt{3})\)

Question 11
112212

Simplify by rationalising the denominator of \(\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\)

\(5+2\sqrt{6}\)

Question 12
112213

Simplify by rationalising the denominator of \(\dfrac{1}{\sqrt{5}-2}+\dfrac{1}{\sqrt{5}+2}\)

\(2 \sqrt{5}\)