The value of 7-3-10-3-2-5-6-5-3-2-15-3-2 is

The correct option is A 1 On rationalizing, we get 7√(3)(√(10)+√(3))×√(10) √(3)√(10) √(3) 2√(5)√(6)+√(5)×√(6) √(5)√(6) √(5) 3√(2)√(15)+3√(2)×√(15) 3√( ...

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Standard X

Mathematics

Trigonometric Identities

The value of ...

Question

The value of $\frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}}$ is

1

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2

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\frac{1}{2}

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3

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Solution

The correct option is A $1$
On rationalizing, we get
$\frac{7 \sqrt{3}}{(\sqrt{10} + \sqrt{3})} \times \frac{\sqrt{10} - \sqrt{3}}{\sqrt{10} - \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} \times \frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} - \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}} \times \frac{\sqrt{15} - 3 \sqrt{2}}{\sqrt{15} - 3 \sqrt{2}}$
$= \frac{7 \sqrt{3} (\sqrt{10} - \sqrt{3})}{7} - \frac{2 \sqrt{5} (\sqrt{6} - \sqrt{5})}{1} - \frac{3 \sqrt{2} (\sqrt{15} - 3 \sqrt{2})}{- 3}$
$= \sqrt{30} - 3 - 2 \sqrt{30} + 10 + \sqrt{30} - 6 = 10 - 9 = 1$

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Similar questions

Q. Show that

\frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}} = 1

Q. Find the value of:

(1) 3⁶
(2) 6³
(3) 2⁶
(4) 1⁸
(5) 5⁴
(6) 4³
(7) 10⁵
(8) 10⁷
(9) 7⁴
(10) 8²

Simplify:

(a)

\frac{2}{3} + \frac{1}{7}

(b)

\frac{3}{10} + \frac{7}{15}

(c)

\frac{4}{9} + \frac{2}{7}

(d)

\frac{5}{7} + \frac{1}{3}

(e)

\frac{4}{5} + \frac{2}{3}

(f)

\frac{3}{4} - \frac{1}{3}

(g)

\frac{5}{6} - \frac{1}{3}

Q. Simplify :

\frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}}

Simplify: $\frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}}$ .

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The value of 7√3√10+√3−2√5√6+√5−3√2√15+3√2 is

The correct option is A 1On rationalizing, we get7√3(√10+√3)×√10−√3√10−√3−2√5√6+√5×√6−√5√6−√5−3√2√15+3√2×√15−3√2√15−3√2=7√3(√10−√3)7−2√5(√6−√5)1−3√2(√15−3√2)−3=√30−3−2√30+10+√30−6=10−9=1

The value of $\frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}}$ is