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How Many Numbers Can Be Formed Using a Certain Number of Digits?

Simplify the ...

Question

Simplify the following expressions:

(i) $(4 + \sqrt{7}) (3 + \sqrt{2})$

(ii) $(3 + \sqrt{3}) (5 - \sqrt{2})$

(iii) $(\sqrt{5} - 2) (\sqrt{3} - \sqrt{5})$

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Solution

(i) We can simplify the expression as

Hence the value of the expression is

(ii) We can simplify the expression as

Hence the value of the expression is

(iii) We can simplify the expression as

Hence the value of the expression is .

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Similar questions

Simplify the following expressions :

(i) $(4 + \sqrt{7}) (3 + \sqrt{2})$

(ii) $(3 + \sqrt{3}) (5 - \sqrt{2})$

(iii) $(\sqrt{5} - 2) (\sqrt{3} - \sqrt{5})$

Q. Simplify the following expressions:

(i)

(11 + \sqrt{11}) (11 - \sqrt{11})

(5 + \sqrt{7}) (5 - \sqrt{7})

(\sqrt{8} - \sqrt{2}) (\sqrt{8} + \sqrt{2})

(3 + \sqrt{3}) (3 - \sqrt{3})

(\sqrt{5} - \sqrt{2}) (\sqrt{5} + \sqrt{2})

Q. Simplify each of the following expressions:
(i)

(3 + \sqrt{3}) (2 + \sqrt{2})

(3 + \sqrt{3}) (3 - \sqrt{3})

(\sqrt{5} + \sqrt{2})^{2}

(\sqrt{5} - \sqrt{2}) (\sqrt{5} + \sqrt{2})

Evaluate:

$(i) 5^{- 2} (i i) (- 3)^{- 2} (i i i) {(\frac{1}{3})}^{- 4} (i v) {(\frac{- 1}{2})}^{- 1}$

Simplify :

(i) $\frac{3 \sqrt{2} - 2 \sqrt{3}}{3 \sqrt{2} + 2 \sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}$

(ii) $\frac{7 + 3 \sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3 \sqrt{5}}{3 - \sqrt{5}}$

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How Many Numbers Can Be Formed Using a Certain Number of Digits?

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