Find the value of 7-77-7- Is it rational- -4 MARKS-

Concept : 1 Mark Rationalisation : 2 Marks Identification : 1 Mark We have, (7+√(7))(7 √(7))=7^2 (√(7))^2 nbsp; = 49 – 7 = 42 [using the identity nbsp; ...

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Standard IX

Mathematics

Operations on Irrational Number

Find the valu...

Question

Find the value of $(7 + \sqrt{7}) (7 - \sqrt{7})$ . Is it rational? [4 MARKS]

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Solution

Concept : 1 Mark
Rationalisation : 2 Marks
Identification : 1 Mark

We have,
$(7 + \sqrt{7}) (7 - \sqrt{7}) = 7^{2} - (\sqrt{7})^{2} = 49 - 7 = 42 [u s i n g t h e i d e n t i t y (a + b) (a - b) = a^{2} - b^{2}]$

42 is a rational number.

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Q. If a and b are rational numbers and

\frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} = a - b \sqrt{77},

find

a - b

If a and b are rational numbers and $\frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} = a - b \sqrt{77},$ find the values of a and b.

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Find the value of (7+√7)(7−√7). Is it rational? [4 MARKS]

Concept : 1 Mark Rationalisation : 2 Marks Identification : 1 Mark We have, (7+√7)(7−√7)=72−(√7)2=49–7=42[using the identity (a+b)(a−b)=a2−b2] 42 is a rational number.

Find the value of $(7 + \sqrt{7}) (7 - \sqrt{7})$ . Is it rational? [4 MARKS]

Concept : 1 Mark
Rationalisation : 2 Marks
Identification : 1 Mark

We have,
$(7 + \sqrt{7}) (7 - \sqrt{7}) = 7^{2} - (\sqrt{7})^{2} = 49 - 7 = 42 [u s i n g t h e i d e n t i t y (a + b) (a - b) = a^{2} - b^{2}]$

42 is a rational number.