999 is a perfect cube. State whether the statement is true (T) or false (F). The given statement is False Explanation Let us do the prime factorisation of 999 to fins if it is a perfect cube or not The prime... View Article
Cube of an odd number is odd. State whether the statement is true (T) or false (F). The given statement is True Explanation The cube of an odd number is always an odd number. 73= 343 93 = 729 Hence, the cube... View Article
Cube of an even number is even. State whether the statement is true (T) or false (F). The given statement is True Explanation The cube of an even number is always an even number. 63= 216 83 = 512 Hence, the cube of an... View Article
Cube of an odd number is even. State whether the statement is true (T) or false (F). The given statement is False Explanation The cube of an odd number is always an odd number. 73= 343 93 = 729 The cube of an odd... View Article
Cube of an even number is odd. State whether the statement is true (T) or false (F). The given statement is False Explanation The cube of an even number is always an even number. 63= 216 83 = 512 The cube of an even number is... View Article
The cube of a one digit number cannot be a two digit number. State whether the statement is true (T) or false (F). The given statement is False Explanation Let us take the number having 7 Its square 43 = 64 The given statement is... View Article
A number having 7 at its ones place will have 3 at the ones place of its cube. State whether the statement is true (T) or false (F). The given statement is True Explanation Let us take the number having 7 at its ones place i.e. 37 and Its square 173 = 4913... View Article
A number having 7 at its ones place will have 3 at the units place of its square. State whether the statement is true (T) or false (F). The given statement is False Explanation Let us take the number having 7 at its ones place i.e.17 and Its square 172 = 289 Hence... View Article
Square root of a number x is denoted by √x. State whether the statement is true (T) or false (F). The given statement is True Explanation The symbol or sign to represent a square root is ‘√’. This symbol is also called... View Article
The square root of a perfect square of n digits will have (n + 1)/2 digits, if n is odd. State whether the statement is true (T) or false (F). The given statement is True Explanation Let au assume the perfect square has 9 digits, then its square root has 5 digits (9 + 1)/2... View Article
If a2 ends in 9, then a2 ends in 7. State whether the statement is true (T) or false (F). The given statement is False Explanation Let a2 be 372 So, 372 = 1369 Then, 373 = 50653 Hence the give... View Article
If a2 ends in 5, then a3 ends in 25. State whether the statement is true (T) or false (F). The given statement is False Explanation Let a2 be 352 So, 352 = 1225 Then, 353 = 42875 Hence the give statement is... View Article
Let x and y be natural numbers. If x divides y, then x3 divides y3. State whether the statement is true (T) or false (F). The given statement is True Explanation If x divides y = y/x is a natural number and then x3 divides y3 = y3/x3 is a... View Article
If x and y are integers such that x2 > y2, then x3> y3. State whether the statement is true (T) or false (F). The given statement is False Explanation Let us consider negative integers -6 and -5 Then, = (-62) > (-52) =... View Article
For an integer a, a2 is always greater than a2. State whether the statement is true (T) or false (F). The given statement is False Explanation Let us take one negative integer, i.e. -3 Then, -33 = -3 × -3 × -3 = -27... View Article
All numbers of a Pythagorean triplet are odd. State whether the statement is true (T) or false (F). The given statement is False Explanation We know that general form of Pythagorean triplet is (2m, m²-1, m²+1) Consider three... View Article
For every natural number m, (2m –1, 2m2 –2m, 2m2 –2m + 1) is a Pythagorean triplet. State whether the statement is true (T) or false (F). The given statement is False Explanation We know that general form of Pythagorean triplet is (2m, m²-1, m²+1) Hence,... View Article
A perfect square can have 8 as its unit’s digit. State whether the statement is true (T) or false (F). The given statement is False Explanation From the properties of square numbers, we know that A number with 2, 3, 7 or 8 at... View Article
1000 is a perfect square. State whether the statement is true (T) or false (F). The given statement is False Explanation It is not a perfect square. Let us find the prime factorization of 1000 1000 = 2 × 2... View Article
The sum of first n odd natural numbers is n2. State whether the statement is true (T) or false (F). The given statement is True Explanation The sum of odd numbers = ∑ (2n – 1) = (2 × n × (n + 1))/2 –n =... View Article
