Question

1. Find five rational numbers between 2 and 3 by mean method ?
2. Express 1.62626262... in the form of p/q where q is not equal to zero and p,q∈Z
3. Represent 8/5 and -8/5 on a number line
4. Explain with an example how irrational numbers differ from rational number
5. Check whether 5√2 is rational or irrational
6. Rationalise the denominator of
6 - 4√2 / 6+4√2
B ) Answer any two of the following 2 ×4 =8
7. Simplify ⁴√ 81 - 8 ³√343 + 15 ⁵√32 + √225
8. If a and b are rational numbers, find the value of a and b in √3 + √2 /√3 - √2 = a + b√6
9. Find the value of √5 upto six decimal places


please tell me correct answers in correct formulaa...
please........​

Answer 1

Answer:

I am providing u the answers only

1. 2.2,2.4,2.6,2.8,2.5
2. 161/99
3. ......cant draw now...
4. root 5 is irrational and 25 is rational. irrational are the numbers that cannot be expressed in the P by Q form where p and q are integers and q is not equal to zero but rational numbers can be expressed in p by Q form where p and q are integers and q is not equal to zero
5. 5√2 is irrational because it cannot be expressed in p by Q form .
6. 52-48√2/20

don't want to solve Next questions

if these help u then it's good

Answer 2

1\ Answer:

“Five rational numbers” between 2 and 3 are : 2.5, 2.25, 2.125, 2.75, 2.875 .

To find:

“5 rational numbers” between 2 and 3 using the mean method

Solution:

A “rational number” is a number which of the form a/b where a and b are integers.

Number 1: Take the “average of 2 and 3”

$=\frac{2+3}{2}=\frac{5}{2}=2.5$

Number 2: Take the “average of 2 and 2.5”

$=\frac{2+2.5}{2}=\frac{4.5}{2}=2.25$

Number 3: Take the “average of 2 and 2.25”

$=\frac{2+2.25}{2}=\frac{4.25}{2}=2.125$

Number 4: Take the “average of 3 and 2.5”

$=\frac{3+2.5}{2}=\frac{5.5}{2}=2.75$

Number 5: Take the “average of 3 and 2.75”

$=\frac{3+2.75}{2}=\frac{5.75}{2}=2.875$

Thus, “5 rational numbers” between 2 and 3 are : 2.5, 2.25, 2.125, 2.75, 2.875 .

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2\Answer:

162626262/100000000

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3\

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$\frac{-9}{5}$  $\frac{-8}{5}$  $\frac{-7}{5}$  $\frac{-6}{5}$  $\frac{-5}{5}$  $\frac{-4}{5}$  $\frac{-3}{5}$  $\frac{-2}{5}$  $\frac{-1}{5}$  $0$  $\frac{1}{5}$   $\frac{2}{5}$   $\frac{3}{5}$   $\frac{4}{5}$   $\frac{5}{5}$   $\frac{6}{5}$   $\frac{7}{5}$   $\frac{8}{5}$

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4\

Numbers that can be expressed as a ratio of two number (p/q form) are termed as a rational number. ... Irrational Numbers includes surds such as √2, √3, √5, √7 and so on.

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5\

$\sqrt[5]{2}$

 

Here 5 is a rational number  

But $\sqrt{2}$=1.4142...., is an irrational number  

Then product of an irrational and rational number is also an irrational number

So $\sqrt[5]{2}$=5×1.4142..=7.0710... is an irrational number

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6\

(6-4√2)/(6+4√2)

Rationalising factor = 6-4√2

(6-4√2)/(6+4√2) × (6-4√2)/(6-4√2)

=(6-4√2)(6-4√2)/(6+4√2)(6-4√2)

=(6-4√2)²/(6²-(4√2)²)

=[6²+(4√2)²-2(6)(4√2)]/(36-16(2))

=(36+16(2)-48√2)/(36-32)

=(36+32-48√2)/4

=(68-48√2)/4

=68/4 - 48√2/4

= 17 - 12√2

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 7\

$=\sqrt[4]{81}=3^{4}=81\\=\sqrt[3]{7}=7^{3}=343\\=\sqrt[5]{2}=2^{5}=32\\=\sqrt{225}=15^{2}=225\\=3-8*7+15*2+15=-8$

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8\

Answer

$=\frac{(\sqrt{3}+(\sqrt{2)} ^{2} }{(\sqrt{3}-\sqrt{2)}(\sqrt{3}+\sqrt{2}) }=A+B\sqrt{6}$

$=\frac{3+2+2\sqrt{6} }{3-2}=A+B\sqrt{6}$

$=5+2\sqrt{6}=A+B\sqrt{6}$

$A=5,B=2$

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9\

2.236067

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HOPE IT HELP YOU