if √2=1.414,√3=1.732 .find the Value of 1/√3+√2
Answers
Answer:
First we have to rationalise the denominator.
\frac{1}{ \sqrt{3} - \sqrt{2} }
3
−
2
1
\frac{1}{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }
3
−
2
1
×
3
+
2
3
+
2
\frac{ \sqrt{3} + \sqrt{2} }{( \sqrt{3} - \sqrt{2})( \sqrt{3} + \sqrt{2} )}
(
3
−
2
)(
3
+
2
)
3
+
2
Using identity : ( a - b) ( a + b) = a² - b²
\frac{ \sqrt{3} + \sqrt{2} }{ {( \sqrt{3} )}^{2} - {( \sqrt{2}) }^{2} }
(
3
)
2
−(
2
)
2
3
+
2
\frac{ \sqrt{3} + \sqrt{2} }{3 - 2}
3−2
3
+
2
\frac{ \sqrt{3} + \sqrt{2} }{1}
1
3
+
2
Putting the value of root 3 and root 2
= 1.732 + 1.414=1.732+1.414
= 3.146=3.146
Answer:
ANSWER
⇒2=1.414,3=1.732
∴33−224 + 33+223
⇒3∗1.732−2∗1.4144+3∗1.732+2∗1.4143
⇒5.196−2.8284+5.196+2.8283
⇒2.3684+8.0243
⇒1.960+0.373=2.063