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

Solution Let us first determine the factors by the method of prime factorization Factors of 216 = 2 × 2 × 2 × 3 × 3... View Article

Write two Pythagorean triplets each having one of the numbers as 5.

Given From the given details one of the numbers in the Pythagorean triplet. Find out We have to determine the... View Article

Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

Solution Let us first determine the factors by the method of prime factorization So, prime factors of 9720 = 2 × 2 × 2 × 3... View Article

Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.

Solution Let us first determine the factors by the method of prime factorization So, prime factors of 176 = 2 × 2 × 2 × 2... View Article

Using prime factorisation, find the cube roots of (a) 512 (b) 2197

Solution (a) 512 Let us first determine the factors by the method of prime factorization So, prime factors of 512 = 2 × 2 × 2... View Article

Using prime factorisation, find the square roots of (a)11025 (b) 4761

Solution (a)11025 Answer Let us first determine the factors by the method of prime factorization Hence the factors obtained of 11025 = 3 ×... View Article

Write the Pythagorean triplet whose one of the numbers is 4.

Given From the given details one of the numbers in the Pythagorean triplet. one of the number in the Pythagorean triplet is 4 Find out We have to... View Article

Can a right triangle with sides 6cm, 10cm and 8cm be formed? Give reason.

Given From the given details we note that The sides of the right angle triangle are 6 cm, 10 cm and 8 cm Find out We have to determine whether... View Article

Using distributive law, find the squares of (a)101 (b) 72

Solution (a)101 Answer On applying the distributive law, we obtain We know that 101 can be expressed as 101 = 100 + 1 So, 1012 = (100... View Article

Using prime factorisation, find which of the following are perfect cubes. (a)128 (b) 343 (c) 729 (d) 1331

Solution (a)128 Answer Let us first determine the factors by the prime factorization method On prime factorisation the factors obtained of... View Article

Using prime factorisation, find which of the following are perfect squares. (a) 484 (b) 11250 (c) 841 (d) 729

Solution (a) 484 Answer Let us first determine the factors by the method of prime factorization Hence the factors obtained of 484 = 2 × 2... View Article

Express 81 as the sum of first nine consecutive odd numbers.

Solution The first nine consecutive odd numbers are 1, 3, 5, 7, 9, 11, 13, 15 and 17 We know that 81 is a perfect square, 81 = (9)2 Now, The... View Article

Show that 500 is not a perfect square.

Solution We have to show that 500 is not a perfect square On prime factorisation of 500 we obatin 500=2 × 2 × 5 × 5... View Article

Write cubes of first three multiples of 3.

Solution The first three multiple of 3 are 3, 6 and 9 Cubes of first three multiples of 3, = 33 = 3 × 3 × 3 = 27 = 63 =... View Article

Write the first five square numbers.

Solution The first five squares of the number are 1 × 1 = 12=1 2 × 2 = 22 =4 3 × 3 =3 2= 9 4 × 4 =42= 16 5... View Article

Square of a number is positive, so the cube of that number will also be positive. State whether the statement is true (T) or false (F).

The given statement is False Explanation Let us take -5 Now, square of the -5 i.e. -52 = 25 Then, cube of the same number i.e.... View Article