Question

What are the properties of cube and square numbers

Answer 1

The property of a cube is that it will always be multiplying a number to the ³ power. Squares always multiply its number to the ² power. A squared number can become a perfect square root, which means its also a rational number. Cubed numbers can become cubed roots, also meaning they are rational.

Answer 2

$\bold{\huge{Answer :-}}$

=>PROPERTIES OF PERFECT SQUARE :–

★A number ending in 2 , 3 , 7 or 8 is never a perfect square .

★A number ending in odd number of zero is never a perfect square .

★The square of an even number is even .

★The square of an odd number is odd .

★The square of a proper fraction is smaller than the fraction .

★For every natural number n , we have {(n + 1)^2 –n^2 } = {( n + 1 )+n}

★Sum of the first " n " odd natural numbers = n^2 .

★If m , n, p are natural numbers such that (m^2 + n^2 ) = p^2 , then ( m , n , p ) is called a Pythagorean triplet ..

★For every natural number m > I , ( 2m , m^2 –1 , m^2 + 1 ) is a Pythagorean triplet.

=>PROPERTIES OF CUBE AND CUBES ROOT .

★The cube of a number is that number raised to be power 3 .

★A natural number n is a perfect cube if n = m^3 for some natural number m .

★The cube of an even natural number is always even .

★The cube of an odd number is odd always.

★The cube root of a number X is the number whose cube is X .It is denoted by =>
$\sqrt[3]{x}$
★For finding the cube root of a perfect cube , resolve it into prime factors : make triplets of similar factors , choosing one out of every triplet .

★For any any positive integer X , we have ,
$\sqrt[3]{ - x} = - \sqrt[3]{x}$
★For any integers a and b , we have : =>
$\sqrt[3]{ab} = \sqrt[3]{a} \times \sqrt[3]{b}$
=>
$\sqrt[3]{a \div b = } \sqrt[3]{a \div \sqrt[3]{b} }$



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