If 3√5 + √125 = 17.88, then what will be the value of √80 + 6√5?

Question

If \(3\sqrt5 \) + \(\sqrt{125}\) = 17.88, then what will be the value of \(\sqrt{80}\) + \(6\sqrt5\) ?

(a) 13.41

(b) 20.46

(c) 21.66

(d) 22.35

Answer 1

(d) 22.35

\(3\sqrt5 \) + \(\sqrt{125}\) = 17.88

\(\Rightarrow\) \(3\sqrt5 \) + \(\sqrt{5^2\times5}\) = 17.88

\(\Rightarrow\) \(3\sqrt5 \) + \(5\sqrt5\) = 17.88

\(\Rightarrow\) \(8\sqrt5 \) = 17.88 \(\Rightarrow\) \(\sqrt5\) = \(\frac{17.88}{8}\) = 2.235

Now, \(\sqrt{80}+6\sqrt5\) = \(\sqrt{16\times5}\) + \(6\sqrt5\) 

= \(4\sqrt5 + 6\sqrt5\) = \(10\sqrt5\)

=10 x 2.235 = 22.35.