3. It being given that 2 = 1.414, V3 = 1.732, V5 = 2.236 and 710 = 3.162,
find the value to three places of decimals, of each of the following.
2
2-√3
√10 - √5
(iii)
[2010]
5
V3
2
can be
Answers
Answer:
The given expressions are evaluated after rationalizing its denominators.
Given:
\sqrt2=1.414,\sqrt3=1.732,\sqrt5=2.236\:and\:\sqrt{10}=3.162
2
=1.414,
3
=1.732,
5
=2.236and
10
=3.162
1.
\frac{2}{\sqrt5}
5
2
=\frac{2}{\sqrt5}*\frac{\sqrt5}{\sqrt5}=
5
2
∗
5
5
=\frac{2\sqrt5}{5}=
5
2
5
=\frac{2(2.236)}{5}=
5
2(2.236)
=\frac{4.472}{5}=
5
4.472
=0.8945=0.8945
2..
\frac{2-\sqrt3}{\sqrt3}
3
2−
3
=\frac{2-\sqrt3}{\sqrt3}*\frac{\sqrt3}{\sqrt3}=
3
2−
3
∗
3
3
=\frac{2\sqrt3-3}{3}=
3
2
3
−3
=\frac{2(1.732)-3}{3}=
3
2(1.732)−3
=\frac{3.464-3}{3}=
3
3.464−3
=\frac{0.464}{3}=
3
0.464
=0.1546=0.1546
3.
\frac{\sqrt{10}-\sqrt5}{\sqrt2}
2
10
−
5
=\frac{\sqrt{10}-\sqrt5}{\sqrt2}*\frac{\sqrt2}{\sqrt2}=
2
10
−
5
∗
2
2
=\frac{\sqrt{20}-\sqrt{10}}{2}=
2
20
−
10
=\frac{2\sqrt{5}-\sqrt{10}}{2}=
2
2
5
−
10
=\frac{2(2.236)-3.162}{2}=
2
2(2.236)−3.162
=\frac{4.472-3.162}{2}=
2
4.472−3.162
=\frac{1.310}{2}=
2
1.310
=0.655=0.655