Question

Evaluate 10.2^3 using suitable identity

Answer 1

(10+.2)^3=(10)^3+(.2)^3+3×10×(.2)[10+0.2]
=1000+0.008+6.0×10.2.
=1000.008+61.2=1061.208

Answer 2

Concept: The exponent of a number indicates how many times a number has been multiplied by itself. For instance, $3^4$ indicates that we have multiplied 3 four times. Its full form is 3 × 3 × 3 × 3. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal.

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

To find: $(10.2)^3$ using suitable identity

Solution:

$(10.2)^{3} = (10+0.2)^3$  [since, 10.2 can be written as 10 + 0.2]

As we know, $(a + b)^3 = a^3 + b^3 +3ab(a+b)$

Here, a = 10 and b = 0.2

Therefore,

$(10+0.2)^3 = (10)^3 + (0.2)^3 + 3(10)(0.2)(10+0.2)\\(10+0.2)^3 = 1000 + 0.008 + 6(10.2)\\(10+0.2)^3 = 1000 + 0.008 + 61.2\\(10+0.2)^3 = 1061.208$

Hence, $(10.2)^3 = 1061.208$

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