it is given that root2=1.414 root3=1. 732 root5=2. 236and root10=3.162 find the value to three places of decimal as number is root10-root5/root2
Answers
Heya friend,
Here is the answer you were looking for:
\begin{lgathered}\frac{ \sqrt{10} - \sqrt{5} }{2 \sqrt{2} } \\\end{lgathered}
2
2
10
−
5
On rationalizing the denominator we get,
\begin{lgathered}= \frac{ \sqrt{10} - \sqrt{5} }{2 \sqrt{2} } \times \frac{2 \sqrt{2} }{2 \sqrt{2} } \\ \\ = \frac{2 \sqrt{2}( \sqrt{10} - \sqrt{5}) }{ {(2 \sqrt{2}) }^{2} } \\ \\ = \frac{2 \sqrt{20} - 2 \sqrt{10} }{8} \\ \\ = \frac{2( \sqrt{20} - \sqrt{10}) }{8} \\ \\ = \frac{ \sqrt{20} - \sqrt{10} }{4} \\\end{lgathered}
=
2
2
10
−
5
×
2
2
2
2
=
(2
2
)
2
2
2
(
10
−
5
)
=
8
2
20
−2
10
=
8
2(
20
−
10
)
=
4
20
−
10
We can write √20 as √2 × √2 × √5
And √10 as √2 × √5
\begin{lgathered}\frac{ \sqrt{5} \times \sqrt{2} \times \sqrt{2} - \sqrt{5} \times \sqrt{2} }{4} \\ \\ = \frac{2.236 \times 1.414 \times 1.414 - 2.236 \times 1.414}{4} \\ \\ = \frac{4.470 - 3.161}{4} \\ \\ = \frac{1.309}{4} \\ \\ = 0.327 \: (approx)\end{lgathered}
4
5
×
2
×
2
−
5
×
2
=
4
2.236×1.414×1.414−2.236×1.414
=
4
4.470−3.161
=
4
1.309
=0.327(approx)
Answer:
0.6548
Step-by-step explanation:
Root10 = 3.162
Root5 = 2.236
Root2 = 1.414
First, subtract root 10 and 5 Then divide it by root2.