If - 6-2- 3 33-19- 3 -a-b- 3 - then a-b-

The correct option is B 8 √(6+2√(3)(33 19√(3))) ⇒√((6+2√(3))(33+19√(3))6) ⇒√(33+11√(3)+19√(3)+19) ⇒√(52+30√(3)) ⇒√(5^2+2(5)(3√(3) ...

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Byju's Answer

Standard IX

Mathematics

Irrational Numbers on the Number Line

If √ 6+2√ 3...

Question

If $\sqrt{\frac{6 + 2 \sqrt{3}}{33 - 19 \sqrt{3}}} = a + b \sqrt{3}$ , then $a + b =$ .....

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Solution

The correct option is B $8$
$\sqrt{\frac{6 + 2 \sqrt{3}}{(33 - 19 \sqrt{3})}}$
$\Rightarrow \sqrt{\frac{(6 + 2 \sqrt{3}) (33 + 19 \sqrt{3})}{6}}$
$\Rightarrow \sqrt{33 + 11 \sqrt{3} + 19 \sqrt{3} + 19}$
$\Rightarrow \sqrt{52 + 30 \sqrt{3}}$
$\Rightarrow \sqrt{5^{2} + 2 (5) (3 \sqrt{3}) + (3 \sqrt{3})^{2}}$
$\Rightarrow \sqrt{(5 + 3 \sqrt{3})^{2}} = 5 + 3 \sqrt{3}$
Hence $a + b = 5 + 3 = 8$

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Similar questions

Q. If

\sqrt{\frac{6 + 2 \sqrt{3}}{33 - 19 \sqrt{3}}} = a + b \sqrt{3},

then

a + b =

If A = {3, 6, 9, 12, 15, 18, 21}
B = {2, 4, 6, 8, 10, 12, 14, 16}
C = {5, 10, 15, 20}

$\begin{matrix} A & B 1. B - C & A . {5, 10, 20} 2. A - C & B . {3, 9, 15, 21} 3. C - (A - B) & C . {3, 6, 9, 12, 18, 21} 4. C \cap (A - B) & D . {15} E . {2, 4, 6, 8, 12, 14, 16} \end{matrix}$

Q. If

A = {2, 3, 4, 8, 10},

B = {3, 4, 5, 10, 12},

C = {4, 5, 6, 12, 14},

then

(A \cup B) \cap (A \cup C)

Q. Simplify:

(- 10 a^{3} b + 12 a^{2} b^{2} - 6 a b^{3}) - (8 a^{3} b + 6 a^{2} b^{2} - 9 a b^{3})

8 a^{3} + b^{3} + 12 a^{2} b + 6 a b^{2}

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If √6+2√333−19√3=a+b√3, then a+b=.....

The correct option is B 8√6+2√3(33−19√3)⇒√(6+2√3)(33+19√3)6⇒√33+11√3+19√3+19⇒√52+30√3⇒√52+2(5)(3√3)+(3√3)2⇒√(5+3√3)2=5+3√3Hence a+b=5+3=8

If $\sqrt{\frac{6 + 2 \sqrt{3}}{33 - 19 \sqrt{3}}} = a + b \sqrt{3}$ , then $a + b =$ .....