Adding and Subtracting Surds - Questions

Question 1

Simplify: \(\sqrt 8 - 6\sqrt 8 + 15\sqrt 8 \)

\(20\sqrt 2 \)

Question 2

Simplify: \(\sqrt {24} + \sqrt {54} \)

\(5\sqrt 6 \)

Question 3

Simplify: \(\sqrt 2 + \sqrt 8 + \sqrt {32} + \sqrt {128} \)

\(15\sqrt 2 \)

Question 4

Simplify: \(5\sqrt 7 + 7\sqrt 5 - \sqrt {20} - \sqrt {28} \)

\(3\sqrt 7 + 5\sqrt 5 \)

Question 5

Simplify: \(\sqrt {999} + \sqrt {99} - \sqrt {444} - \sqrt {44} \)

\(\sqrt {111} + \sqrt {11} \)

Question 6

Simplify \(\sqrt{5}+4 \sqrt{5}-2 \sqrt{5}\)

\(3 \sqrt{5}\)

Question 7

Simplify \(4\sqrt{2}- \sqrt{3}+2 \sqrt{2}-\sqrt{3}\)

\(6 \sqrt{2}-2 \sqrt{3}\)

Question 8

Simplify \(\sqrt{20}+ \sqrt{45}\)

\(5 \sqrt{5}\)

Question 9

\(\sqrt{20}+\sqrt{5}=\sqrt{x}\). Find \(x\)

\(x=45\)

Question 10

\(\sqrt{112}-\sqrt{28}=\sqrt{x}\). Find \(x\)

\(x=28\)