Finding the Square of a Number

Q.

Is 90 a perfect square? [3 MARKS]

Q.

A perfect square number has four digits, none of which is zero. The digits from left to right have values, that are even, even, odd, even. Find the number.

Q. What is the square root of 12.25?

1. 3.5
2. 3.6
3. 3.2
4. 3.9

Q.

180 is a perfect square.

Q. There are natural numbers between ${17}^2$ and ${18}^2$

1. 30
2. 32
3. 34
4. 36

Q.

Find the smallest number by which 9408 must be divided so that the quotient is a perfect square. Find the square root of the quotient.

Q. What is the smallest natural number which when added to the difference of squares of 17 and 13 gives a perfect square?

1. 5
2. 11
3. 24
4. 1

Q.

Akanksha was asked to multiply a number by its successor. But she was careless and multiplied the number with itself. When she rechecked, she found the error and added the original number to the final result. The result is ___(less/more/equal to) the actual correct answer.

Q.

What is the square of $2\frac{3}{4}$ ?

1. $\frac{9}{16}$

2. $\frac{121}{16}$

3. $\frac{121}{8}$

4. $\frac{13}{16}$

Q. Square of any number from 25 to 75 can be found by following three simple steps:-

Step 1:- Subtracting 25 from the number.
Step 2:- Subtracting the number from $x$ and then taking the square of it.
Step 3:- Combining the results obtained in step 1 and step 2.

What is the value of $x$ ?

1. 25
2. 50
3. 75
4. 100

Q.

Column I	Column II
Greatest 3 digit perfect square	$1,024$
Smallest 5 digit perfect square	$9,801$
Smallest 3 digit perfect square	$961$
Greatest 4 digit perfect square	$10,000$
Smallest 4 digit perfect square	$100$

Q. The square of which of the following number will be even?
11, 111, 1111, 112

1. 111
2. 1111
3. 112
4. 11

Q.

Question 9

Write the correct answer from the given four options.

Which letter best represents the location of $\sqrt{25}$ on a number line?

a) A
b) B
c) C
d) D

Q. Find the perfect squares between 40 and 50.​

Q.

Just by looking at the numbers, identify which of the following cannot be a perfect square.

1. 382

2. 484

3. 576

4. 529

Q.

Square numbers can only have _________ numbers in the unit place.

Q.

Question 140

The perimeters of two squares are 40 m and 96 m, respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

Q. What is the square root of 12.25?

1. 3.5
2. 3.6
3. 3.2
4. 3.9

Q. How can ${13}^2$ be written as the sum of two consecutive natural numbers?

Q.

Number of non-square numbers between the squares of 44 and 45 is:

1. 70

2. 100

3. 88

4. 90

Q. What is the value of $(51{)}^2–(49{)}^2$?

1. 300
2. 200
3. 100
4. 50

Q.

Question 55

State whether the following statement is true or false:

The square of 2.8 is 78.4.

Q.

Find the number of digits in the square root of each of the following numbers (without any calculation).

(i) 64 (ii) 144

(iii) 4489 (iv) 27225

(v) 390625

Q.

Question 101

By what smallest number should 216 be divided so that the quotient is a perfect square? Also, find the square root of the quotient.

Q.

What is the square of $3\frac{2}{5}$?

1. $\frac{289}{5}$

2. $\frac{17}{25}$

3. $\frac{289}{25}$

4. $\frac{17}{5}$

Q.

Question 40

Fill in the blanks to make the statements true.

The sides of a right-angled triangle whose hypotenuse is 17 cm are ___ and ___.

Q. A perfect square number has four digits , none of which is zero. The digits from left to right have values that are :even, even, odd, even. Find the number. If the number is 8836. Tell why and how did you get it .

Q. Find the square root of $100$ and $169$ by the method of repeated subtraction.

Q.

Question 89

Solve the following question:

Show that 500 is not a perfect square.

Q. If $T=2\pi \sqrt{\frac{L}{g}}$, then ‘L’ is equal to

1. $\frac{T^2}{2\pi g}$
   
   
2. $\frac{T^{2}g}{2\pi }$
   
3. $\frac{T^{2}g}{2{\pi }^2}$
   
4. $\frac{T^{2}g}{4\pi }$