Question

If root 5 = 2.236 ,root 3= 1.732 find 2/ ( root 5+ root 3) + 7/(root 5-root 3 )

Answer 1

2/(√5+√3)+7/(√5-√3)
={2(√5-√3)+7(√5+√3)}/(√5+√3)(√5-√3)
=(2√5-2√3+7√5+7√3)/{(√5)²-(√3)²}
=(9√5-5√3)/(5-3)
={(9×2.236)-(5×1.732)}/2
=(20.124-8.66)/2
=11.464/2
=5.732 Ans.

Answer 2

Given: $\sqrt{5}=2.236 \text { and } \sqrt{3} =1.732$

$\begin{aligned} & \frac{2}{\sqrt{5}+\sqrt{3}}+\frac{7}{\sqrt{5}-\sqrt{3}} \\=& \frac{2(\sqrt{5}-\sqrt{3})+7(\sqrt{5}+\sqrt{3})}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})} \\=& \frac{2 \sqrt{5}-2 \sqrt{3}+7 \sqrt{5}+7 \sqrt{3}}{(\sqrt{5})^{2}-(\sqrt{3})^{2}} \\ &=\frac{9 \sqrt{5}+5 \sqrt{3}}{2} \\ &=\frac{9 \sqrt{5}+5 \sqrt{3}}{2} \\ &=\frac{9 \sqrt{5}}{2}+\frac{5 \sqrt{3}}{2} \end{aligned}$

$\begin{array}{c}{=\frac{9 \times 2.236}{2}+\frac{5 \times 1.732}{2}} \\\\ {=\frac{20.124}{2}+\frac{8.66}{2}} \\ {=10.062+4.33} \\ \bold{{=14.392}\end{array}}$

The second root is always called as the square root and the third root is always called as the cube root. The root is the number which multiplies itself and leaves the remainder zero.