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

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