Question

Find the value of (103)³ using a suitable identity​

Answer 1

Answer:

(103)³ = 1092727

Step-by-step explanation:

Given,

(103)³

It can be written as (100 + 3)³

Using the identity : (a + b)³ = a³ + b³ + 3ab(a+b)

here, a = 100 and b = 3

(100 + 3)³

= (100)³ + (3)³ + 3*100*3(100+3)

= 1000000 + 27 + 900*103

=  1000027 +92700

= 1092727

Therefore, (103)³ = 1092727.

Answer 2

The value of (103)³ will be 1092727.

Given,

(103)³.

To find,

Value of (103)³, using a suitable identity.

Solution,

In the given problem, it is required to find the value of (103)³ with the help of a suitable identity.

Now, we can see that (103)³ can be written as follows.

$(103)^3=(100+3)^{3} \hfill ...(1)$

There are various algebraic identities in mathematics, the one among those, suitable for the given problem, could be

$(a+b)^{3} =a^{3} +b^{3} +3ab(a+b) \hfill ...(2)$

So, using the identity in (2) above, the value of the expression in (1) can be determined as follows.

Here, we can see,

$a=100,\\b=3.$

Thus,

$(100+3)^{3} =(100)^{3} +(3)^{3} +3(100)(3)(100+3)$

$\implies (100+3)^{3} =(1000000) +(27) +(900)(103)$

$\implies (100+3)^{3} =1000000 +27 +92700$

$\implies (100+3)^{3} =1000000 + 92727$

$\implies (100+3)^{3} =1092727.$

⇒ (103)³ = 1092727.

Therefore, the value of (103)³ will be 1092727.

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