Question

Find square of 101 without doing actual multiply​

Answer 1

Answer

☞ (101)² = 10201

\rule{110}1

To Find

➢ The square of 101 without actual multiplication

\rule{110}1

Steps

(101)² can be written as (100+1)²

We us the identity,

✪ (a + b)² = a² + 2ab + b²

➳ (100 + 1)²

➳ (100)² + 2 * 1 * 100 + (1)²

➳ 10000 + 200 + 1

➳ 10201

\rule{95}1

∙More identities

◕ (a-b)² = a² - 2ab + b²

◕ (a+b)(a-b) = a² - b²

◕ (a+b)³ = a³ + b³ + 3ab(a+b)

\rule{170}3

Answer 2

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: QuEsTiOn :- \: \star}}}}}$

Find the square of 101 without doing actual multiplication

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

$\large{\underline{\boxed{\sf (101)^2 = 10201}}}$

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

We need to find the value of (101)² without doing actual multiplication. Here we go :

⇒ (101)²

It can be written as -

⇒ (100 + 1)²

Now, using identity :

(a + b)² = a² + 2ab + b²

⇒ (100 + 1)²

⇒ (100)² + 2 * 1 * 100 + (1)²

⇒ 10000 + 200 + 1

⇒ 10201

Hence, the value of (101)² is 10201.

$\mathfrak{\huge{\purple{\underline{\underline{Verification}}}}}$

⇒ (101)²

⇒ 101 * 101

⇒ 10201

$\huge\bold\star\blue{Hence}\star$

The answer is 10201.