Question

represent following on number line
$(i) \sqrt{18}$
$(ii) \sqrt{5.6}$
$(iii) \sqrt{13}$
$(iv) \sqrt{6.7}$
$(v) \sqrt{29}$
whoever will give perfect example will be marked as brainliest ​

Answer 1

(1)√18

To find the square root of 18 firstly we will find the prime factorization of 18

18 = 2 × 3 × 3

18 = 2 × 32

Now this can be simplified into √18 = √(2 × 32)

√18 = √2 × √32

√18 = 3√2

Therefore, the square root of 18 can be simplified as √18 = 3√2

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(2)√5.6

First, let's translate this into math:

$\frac{5}{ \sqrt{6} }$

To simplify this, we need to rationalize, or simplify the denominator so that it only contains rational numbers. To do so, multiply both the numerator and denominator by

$\frac{5}{ \sqrt{6} } . \frac{ \sqrt{6} }{ \sqrt{6} }$

$= \frac{5 \sqrt{6} }{ \sqrt{36} }$

$= \frac{5 \sqrt{6} }{6}$

The answer in decimal form (rounded to nearest hundredth's place) is

≈2.04

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(3)√13

The square root of 13 rounded to the nearest tenth, means that you want one digit after the decimal point. The square root of 13 rounded to the nearest hundredth, means that you want two digits after the decimal point. The square root of 13 rounded to the nearest thousandth, means that you want three digits after the decimal point.

10th: √13 ≈ 3.6

100th: √13 ≈ 3.61

1000th: √13 ≈ 3.606

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(4)√6.7

• ³√6.7 is the cube root of 6.7 symbol
• 3 is the index
• 6.7 = radicand; the radicand is the number below the radical sign
• Cube root = 1.885203631
• √ is called radical symbol or radical only

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(5)√29

Highest perfect square less than 29 is 25.

Thus square root of 29 should be greater than 5 but less than 6, since 6^2 equals 36 which is greater than 29.

Assume square root of 29 to be 5.

Divide 29 by 5.

We get 5.8

The more accurate square root would be closer to average of the assumed square root (which in our case was 5) and 29/(assumed square root) , that is (5.8 + 5)/2 = 5.4

Thus 5.4 is a more closer square root.

Now Find 29/5.4 which equals 5.37037 (aooriximately).

Now find average of 5.4 and 5.37037 that is (5.4 + 5.37037)/2 = 5.385185

5.385185 is a much closer value to square root of 29.

Now find ((29/5.385185) + 5.385185)/2 = 5.385164807172 which is correct upto first 10 decimal digits.