(111)^2 can also be written as (100+11)^2 Now, it is of the form (a+b)^2=a^2+b^2+2ab ⇒ (100+11)^2=(100)^2+(11)^2+2× 100×11 ⇒ (100+11)^2=10,000+121+2200 ⇒ (1 ...

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Standard VIII

Mathematics

Application of Identity: (x+y)^2

The value of ...

Question

The value of $(111)^{2}$ is

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Solution

$(111)^{2}$ can also be written as $(100 + 11)^{2}$

Now, it is of the form $(a + b)^{2} = a^{2} + b^{2} + 2 a b$

$\Rightarrow (100 + 11)^{2} = (100)^{2} + (11)^{2} + 2 \times 100 \times 11$

$\Rightarrow (100 + 11)^{2} = 10, 000 + 121 + 2200$

$\Rightarrow (100 + 11)^{2} = 12, 321.$

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Similar questions

Q. The value of

\frac{(119)^{2} + (119) (111) + (111)^{2}}{(119)^{3} - (111)^{3}}

is:

Q. Find the value of

1111^{2}

if:

1^{2} = 1

11^{2} = 121

111^{2} = 12321

119^{2} - 111^{2}

is :

Q. Mark (✓) against the correct answer

(3 \frac{1}{4} - 2 \frac{1}{3}) = ?

(a)

1 \frac{1}{12}

(b)

\frac{1}{12}

(c)

1 \frac{1}{11}

(d)

\frac{11}{12}

Q. Multiplication of

111_{2}

101_{2}

is?

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The value of (111)2 is

(111)2 can also be written as (100+11)2 Now, it is of the form (a+b)2=a2+b2+2ab ⇒(100+11)2=(100)2+(11)2+2×100×11 ⇒(100+11)2=10,000+121+2200 ⇒(100+11)2=12,321.

The value of $(111)^{2}$ is

$(111)^{2}$ can also be written as $(100 + 11)^{2}$

Now, it is of the form $(a + b)^{2} = a^{2} + b^{2} + 2 a b$

$\Rightarrow (100 + 11)^{2} = (100)^{2} + (11)^{2} + 2 \times 100 \times 11$

$\Rightarrow (100 + 11)^{2} = 10, 000 + 121 + 2200$

$\Rightarrow (100 + 11)^{2} = 12, 321.$