(A) Given the expression: $(\sqrt{5}+3)^{2} = a+b\sqrt{5}$.Using the algebraic identity $(x+y)^{2} = x^{2} + 2xy + y^{2}$,where $x = \sqrt{5}$ and $y

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(A) Given the expression: $(\sqrt{5}+3)^{2} = a+b\sqrt{5}$.Using the algebraic identity $(x+y)^{2} = x^{2} + 2xy + y^{2}$,where $x = \sqrt{5}$ and $y = 3$:$(\sqrt{5})^{2} + 2(\sqrt{5})(3) + (3)^{2} = a+b\sqrt{5}$.$5 + 6\sqrt{5} + 9 = a+b\sqrt{5}$.$14 + 6\sqrt{5} = a+b\sqrt{5}$.By comparing the rational and irrational parts on both sides,we get $a = 14$ and $b = 6$.

Class 9 Mathematics Number Systems Mix Examples - Number Systems

Medium

For each question,select the proper option from four options given,to make the statement true: If $(\sqrt{5}+3)^{2}=a+b \sqrt{5}$,then........

A
$a=14, b=6$
B
$a=8, b=3$
C
$a=14, b=3$
D
$a=8, b=6$

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Mix Examples - Number Systems

Write the following in decimal form and state what kind of decimal expansion each has:
$\frac{2}{11}$

Medium

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For each question,select the proper option from the four options given to make the statement true: $(\sqrt{5}+3)^{2}$ is a / an $\ldots \ldots \ldots$ number.

Easy

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Convert the following rational number into decimal form and state the kind of its decimal expansion: $\frac{71}{125}$

Medium

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Express $0.7\overline{39}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Medium

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Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three places of decimal.
$\frac{6}{\sqrt{6}}$

Difficult

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For each question,select the proper option from four options given,to make the statement true: If $(\sqrt{5}+3)^{2}=a+b \sqrt{5}$,then........

Similar Questions

Write the following in decimal form and state what kind of decimal expansion each has:$\frac{2}{11}$

For each question,select the proper option from the four options given to make the statement true: $(\sqrt{5}+3)^{2}$ is a / an $\ldots \ldots \ldots$ number.

Convert the following rational number into decimal form and state the kind of its decimal expansion: $\frac{71}{125}$

Express $0.7\overline{39}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three places of decimal.$\frac{6}{\sqrt{6}}$

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Write the following in decimal form and state what kind of decimal expansion each has:
$\frac{2}{11}$

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three places of decimal.
$\frac{6}{\sqrt{6}}$