Simplify the following. (a) √(162)- √(72) (b) 4√12 - √50 - 5√48 (c) √80 + √125 (d) 1/√5 - 1

Question

Simplify the following.

(a) \(\sqrt{162}-\sqrt{72}\) 

√(162) - √(72)

(b) \(4\sqrt{12}-\sqrt{50}-5\sqrt{48}\)

(c) \(\sqrt{80}+\sqrt{125}\)

(d) \(\frac{1}{\sqrt{5}-1}\)

(e) \(\frac{3}{2\sqrt{3}-\sqrt{2}}\)

(f) \(\frac{5}{2\sqrt{7}-3\sqrt{5}}\)

Answer 1

(a) \(\sqrt{81\times2}-\sqrt{36\times2}=9\sqrt{2}-6\sqrt{2}=3\sqrt{2}\)

(b) \(4\sqrt{4\times3}-\sqrt{25\times2}-5\sqrt{12\times4}\)

\(=8\sqrt{3}-5\sqrt{2}-20\sqrt{2}\)

\(=-12\sqrt{3}-5\sqrt{2}\)

(c) \(\sqrt{16\times5}-\sqrt{25\times5}=4\sqrt{5}-5\sqrt{5}=9\sqrt{5}\)

(d)

(f)

(g)