​ Find the value of √13 + √1300 +√0.013 .(a) 36.164 (b) 37.304 (c) 36.304 (d) 37.164

Question

Assume that \(\sqrt {13}\) = 3.605 (approx.) and \(\sqrt{130}\) = 11.40 (approx.). 

Find the value of \(\sqrt{1.3}\) + \(\sqrt {1300}\) + \(\sqrt {0.013}\) 

(a) 36.164 

(b) 37.304 

(c) 36.304 

(d) 37.164

Answer 1

(b) 37.304

\(\sqrt{1.3} +\sqrt{1300}+\sqrt{0.013}\)

= \(\sqrt{\frac{130}{100}}\) + \(\sqrt{13\times100}\) + \(\sqrt{\frac{130}{10000}}\)

= \({\frac{\sqrt{130}}{\sqrt{100}}}\) + \(\sqrt{13}\) x \(\sqrt{100}\) + \(\frac{\sqrt{130}}{\sqrt{10000}}\)

= \(\frac{11.40}{10}\) + 3.605 x 10 + \(\frac{11.40}{100}\) 

= 1.14 + 36.05 + 0.114 = 37.304