- 11-4- 7 - - 8-2- 7 is equal to-

The correct option is B 3 √( 11+4√( 7 ) nbsp; ) nbsp;√( 8 2√( 7 ) nbsp; ) =√( 7+4+2(2√( 7) ) nbsp; ) nbsp;√( 7+1 2√( 7) ) nbsp; ...

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Byju's Answer

Standard IX

Mathematics

Identity - 1 (Irrational Numbers) 1

√ 11+4√ 7 - √...

Question

$\sqrt{11 + 4 \sqrt{7}} - \sqrt{8 - 2 \sqrt{7}}$ is equal to____.

0

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3

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1

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\sqrt{7}

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None of these

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Solution

The correct option is B $3$
$\sqrt{11 + 4 \sqrt{7}} - \sqrt{8 - 2 \sqrt{7}}$
$= \sqrt{7 + 4 + 2 (2 \sqrt{7)}} - \sqrt{7 + 1 - 2 \sqrt{7)}}$
$= \sqrt{(\sqrt{7)^{2} + (2)^{2} + 2 (\sqrt{7}) (2)}} - \sqrt{(\sqrt{7)^{2} + (1)^{2} + 2 (\sqrt{7}) (1)}}$
$= \sqrt{(\sqrt{7 + 2)^{2}}} - \sqrt{(\sqrt{7 - 1)^{2}}}$
$= \sqrt{7} + 2 - (\sqrt{7} - 1)$
$= \sqrt{7} + 2 - (\sqrt{7} - 1)$
$= 3$

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Similar questions

Evaluate :

$(i) \frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9} (i i) \frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5} (i i i) \frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{9} (i v) \frac{3}{8} + \frac{- 5}{12} + \frac{3}{7} + \frac{3}{12} + \frac{- 5}{8} + \frac{- 2}{7}$

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) $\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}$

(ii) $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$

(iii) $\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}$

(iv) $\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$

Find the medians of following data sets.

Set I -- {3, 7, 2, 11, 8}

Set II -- {-1, 0, 1, 7, 11, 4}

Q. Write the proper sign, < or >, in the empty boxes.

(1)

+ 1 + 6

(2)

- 8 - 5

(3)

- 5 - 8

(4)

- 2 + 3

(5)

+ 3 - 2

(6)

- 1 + 1

(7)

0 - 7

(8)

- 4 + 4

(9)

+ 2 - 6

(10)

- 3 0

(11)

- 6 + 5

(12)

0 + 7

Name the property of multiplication illustrated by each of the following statements :

(i) $\frac{- 15}{8} \times \frac{- 12}{7} = \frac{- 12}{7} \times \frac{- 15}{8}$

(ii) $(\frac{- 2}{3} \times \frac{7}{9}) \times \frac{- 9}{5} = \frac{- 2}{3} \times (\frac{7}{9} \times \frac{- 9}{5})$

(iii) $\frac{- 3}{4} \times (\frac{- 3}{4} \times \frac{- 5}{6}) + (\frac{- 3}{4} \times \frac{7}{8})$

(iv) $\frac{- 16}{9} \times 1 = 1 \times \frac{- 16}{9} = \frac{- 16}{9}$

(v) $\frac{- 11}{15} \times \frac{15}{- 11} = \frac{15}{- 11} \times \frac{- 11}{15} = 1$

(vi) $\frac{- 7}{5} \times 0 = 0$

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√11+4√7−√8−2√7 is equal to____.

The correct option is B 3√11+4√7−√8−2√7=√7+4+2(2√7)−√7+1−2√7)=√(√7)2+(2)2+2(√7)(2)−√(√7)2+(1)2+2(√7)(1)=√(√7+2)2−√(√7−1)2=√7+2−(√7−1)=√7+2−(√7−1)=3

$\sqrt{11 + 4 \sqrt{7}} - \sqrt{8 - 2 \sqrt{7}}$ is equal to____.