Question

Pls give all the answers of the above attachment....​

Answer 1

Step-by-step explanation:

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${ \huge{ \underline{ \boxed{ \textsf{ \textbf{Answer:-}}}}}}$

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6) Given :

• Two Rational number are 5/7 and 9/11

To Find :

• Three Rational number between 5/7 and 9/11

Solution :

First take LCM for 7 and 11

•°• LCM of 7 and 11 is 77

now,

$: \implies \sf \: \frac{5}{7} \: \: and \: \: \frac{9}{11}$

For denominator 77 , we should multiply 7 by 11 and 11 by 7

$: \implies \sf \: \frac{5 \times 11}{7 \times 11} \: \: and \: \: \frac{9 \times 7}{11 \times 7}$

$: \implies \sf \: \frac{55}{77} \: \: and \: \: \frac{63}{77}$

${ \underline{ \boxed{ \sf{ \red{ Rational \: \: \: number \: between \: \frac{5}{7} \: \: and \: \: \frac{9}{11} \: \: is \: \: \frac{56}{77} \: , \frac{57}{77} , \: \frac{58}{77} ...}}}}}$

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7) To Find :

• Rationalizing factors of ³√49

Solution :

$\bf \: 49 \: \implies \: \: we \: \: can \: \: write \: \: as \: {7}^{2}$

$\boxed{ \pink {\sf{49 = {(7)}^{2} }}}$

• To get cube root , we need a product of 3 similar numbers .
• But here we have two 7s, and we need one more 7 inside a cube root
• So, we have to multiply ³√49 by ³√7

$\tt \implies \red{ \sqrt[3]{ {7}^{2} } \times \sqrt[3]{7} = {7}^{ \frac{2}{3} } \times {7}^{ \frac{1}{3} } = {7}^{ \frac{2}{3} + \frac{1}{3} } = {7}^{ \frac{3}{3} } = 7}$

•°• The rationalizing factors of ³√49 is ³√7

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8) To Find :

• Express 4/√5-1 in Rational denominator

Solutions :

Rational denominator of √5-1 is √5+1

$: \implies \sf \: \frac{4}{ \sqrt{5} - 1 }$

$: \implies \sf \: \frac{4}{ \sqrt{5} - 1} \times \frac{ \sqrt{5} + 1}{ \sqrt{5} + 1 }$

$: \implies \sf \: \frac{4( \sqrt{5} - 1) }{ {( \sqrt{5}) }^{2} - {(1)}^{2} }$

$: \implies \sf \: \frac{4 \sqrt{5} + 4}{25 - 1}$

$: \implies \sf \: \frac{4 \sqrt{5} - 4}{24}$

$: \implies \sf \: \frac{ \cancel4 \sqrt{5} - 4}{ \cancel{24} \: \: \: \: 12 }$

${\underline{ \boxed{ : \implies {\sf {\purple{ \frac{ \sqrt{5} + 4}{12}}}}}}}$

Formula Used :

• (a+b)(a-b) = a²-b²

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9)Question :

How many Rational number are there between two Rational number ?

Answer :

• There are Infinity many Rational numbers are there between two Rational numbers

• Eg : 5/10 and 6/10

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10) Given :

• a = 1+√7

To Find :

• Find the value of a in -6/a

Solution :

=> -6/a

=>-6/1+√7 *1-√7/1-√7

=>-6(1-√7)/(1)²-(√7)²

=>-6+6√7/1-7

=>-6+6√7/-6

=>6(-1+√7)/-6

=>-(-1+√7)

=>1-√7

${\underline{ \boxed{ : \implies {\sf {\purple{ a = 1-\sqrt{7}}}}}}}$

Formula Used :

• (a+b)(a-b) = a²-b²

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$\huge{\underline{\boxed{\sf{\green{@\: MagicalLove}}}}}$

Answer 2

Step-by-step explanation:

Given :

Two Rational number are 5/7 and 9/11

To Find :

Three Rational number between 5/7 and 9/11

Solution :

First take LCM for 7 and 11

•°• LCM of 7 and 11 is 77