Geometric Estimation Value of Square Root

Q.

If $\sqrt{13-a\sqrt{10}}=\sqrt{8}+\sqrt{5}$, then a =

1. -5

2. -6

3. -4

4. -2

Q.

If $x=7+4\sqrt{3}$ and xy = 1, then $\frac{1}{x^2}+\frac{1}{y^2}=$

1. 64

2. 194

3. 134

4. $\frac{1}{49}$

Q.

If $x=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}andy=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}},$ then $x^2+xy+y^2=$

1. 101

2. 99

3. 98

4. 102

Q.

Simplify: $(0.0001{)}^{\frac{-3}{4}}$

1. 20

2. ${10}^{-3}$

3. 1000

4. 100

Q.

Rationalize the denominators of $\frac{1}{\sqrt{7}}$

Q.

The numbers 4/15 and 3/10 lie between 1/4 and 1/3.

True or false. Give reasons

Q.

Area of a square whose perimeter is 36 cm is

1. 324 cm²

2. 81 cm²

3. 36 cm²

4. 12 cm²

Q. Which of these numbers lie between root 5 and root 10?

1. 8
2. 4
3. 6
4. 3

Q.

Find the perimeter of the square ABCD?

1. 16 cm

2. 8 cm

3. 4 cm

4. 2 cm

Q.

The diagonal of a square is 10 cm. Its area is:

1. 20 cm²

2. 25 cm²

3. 100 cm²

4. 50 cm²

Q. Find the square root of 3665 using long divison method?

Q. The length of a side of a square of area 25 sq cm is:

1. 4 cm
2. 2 cm
3. 5 cm
4. 3 cm

Q. Find a rational number lying between
(i)
(ii)
(iii) 1.3 and 1.4
(iv) 0.75 and 1.2
(v)
(vi)

Q.

Question 2 (iv)
Find : ${125}^{\frac{-1}{3}}$

Q. The approximated value of $\sqrt{2}$ is.

1. 1.1421...
2. 1.4142...
3. 1.4241...

Q. The area of square is 5 sq units. Calculate the length of each side.

1. 1.41 cm
2. 1.73 cm
3. 2.23 cm
4. 2.64 cm

Q. If $\frac{3+\sqrt{5}}{2\sqrt{5}+3}=a+b\sqrt{5}$, then the numbers $a$ and $b$ are:

1. 
2. 
3. 
4. 

Q. The approximated value of $\sqrt{3}$ is.

1. 1.732...
2. 1.832...
3. 1.532...

Q.

The sides of a square are 4 centimetres long. The midpoints of the sides are joined to form another square as shown below

What is the perimeter of the smaller square?

Q.

$\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}}$=__________.

1. 0

2. 1

3. 2

4. -1

Q.

If $\frac{\sqrt{3}-1}{\sqrt{3}+1}=a-b\sqrt{3}$, then

1. $a=2,b=-1$

2. $a=2,b=1$

3. $a=b=1$

4. $a=-2,b=1$

Q.

The area of a square field is 8 hectares how long wooden men take to cross a diagonally by walking at the rate of 4 km per hour

Q. The length of the side of a square of area 81 sq cm is ___.

1. 7 cm
2. 6.5 cm
3. 9 cm
4. 9.5 cm

Q.

How many square tiles, each of side 25 cm, will be needed to pave a plot 20 m by 12 m?

1. 500

2. 3840

3. 960

4. 4000

Q.

Which of the following is the approximated value of $\sqrt{2}$?

1. 1.4142.................

2. 1.1142.................

3. 1.5142.................

4. 1.2142.................

Q.

The length of the hypotenuse of a right triangle is $\sqrt{3}$ m.Lengths of other two sides are 1 m and $\sqrt{2}$ m respectively. To approximate the value of the new number $\sqrt{3}$, we need to select the numbers and square them to see if its equal to 3.which of the following is the range of numbers we can select?

1. $\sqrt{2}$ >hypotenuse > $\sqrt{2}+1$

2. $\sqrt{2}$ <hypotenuse < $\sqrt{5}+1$

3. $\sqrt{1}$ <hypotenuse < $\sqrt{2}+1$

4. $\sqrt{2}$ <hypotenuse < $\sqrt{2}+1$

Q.

What is the square root of $\mathrm{x}$ squared?

Q.

Which of the following is the approximated value of $\sqrt{3}$?

1. 1.332.................

2. 1.532.................

3. 1.832.................

4. 1.732.................

Q.

$\sqrt{10}\times \sqrt{15}=$

1. $6\sqrt{5}$

2. $5\sqrt{6}$

3. $25$

4. $10\sqrt{5}$

Q.

Which of the following statements is true about the decimal expansion of the square root of 2?

1. finite decimal number

2. non terminating, non repeating

3. 1.41421

4. non terminating, repeating