Multiplying and Dividing Surds - Questions

Question 1

Simplify: \(5\sqrt 3 \times 3\sqrt 5 \)

\(15\sqrt {15} \)

Question 2

Simplify: \(\dfrac{{15\sqrt {10} }}{{10\sqrt {15} }}\)

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

Question 3

Simplify: \(\dfrac{{5\sqrt {18} }}{{24\sqrt {175} }}\)

\(\dfrac{{\sqrt 2 }}{{8\sqrt 7 }}\)

Question 4

Simplify: \( - \sqrt {96} \times \left( { - \sqrt {63} } \right)\)

\(12\sqrt {42} \)

Question 5

Simplify : \(\sqrt {{y^3}} \times \sqrt {45x{y^2}} \times \sqrt {80y{x^3}} \)

\(60{x^2}{y^3}\)

Question 6

Simplify \(\sqrt{20} \times \sqrt{63}\)

\(6 \sqrt{35}\)

Question 7

Simplify \(\dfrac{\sqrt{48}}{\sqrt{75}}\)

\(\dfrac{4}{5}\)

Question 8

Simplify \(\dfrac{2\sqrt{45}}{3\sqrt{5}}\)

2

Question 9

Simplify \(- \sqrt{24} \times \sqrt{96}\)

\(-48\)

Question 10

\(\dfrac{\sqrt{x(x+y)^2} \times \sqrt{x^2(x+y)}}{\sqrt{x(x+y)}}=\)

\(x(x+y)\)