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Chapter 2: Q23. (page 66)

Evaluate the expression whena  =  9  and  b  =  -  4.

3a+b2+13

Short Answer

Expert verified

The value of expression is 56.

Step by step solution

01

Step-1 – What are real numbers? 

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

02

Step-2 – Associative Property of Addition of Real Numbers: 

Suppose a, b, and c is three real numbers.

Associative property of Addition: (a + b) + c = a + (b + c)

If you are adding three real numbers, the sum is always the same regardless of their grouping.

Example: (11+12) + 13 = 11 + (12+13) = 36

03

Step-3 – Evaluate the expression

Associative property of Addition states, if you are adding three real numbers, the sum is always the same regardless of their grouping.

Evaluate the expression:

To evaluate the expression3a+b2  +13, substitute the value of a as 9 and the value of b as – 4 and addition of the numbers as shown below,

localid="1649347331485" 3a+b2 â¶Ä‰+133(9)+-4-4+13 â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰(substitute â¶Ä‰a â¶Ä‰=9 â¶Ä‰and â¶Ä‰b â¶Ä‰= â¶Ä‰âˆ’ 4 )27+ â¶Ä‰16 â¶Ä‰+13(27+ 16)+13 â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰(Associative â¶Ä‰Property â¶Ä‰of â¶Ä‰Addition)27 â¶Ä‰+ â¶Ä‰( â¶Ä‰16 â¶Ä‰+ â¶Ä‰13) â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰(Associative â¶Ä‰Property â¶Ä‰of â¶Ä‰Addition)27+29=56 â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰(addition)

Thus, the value of the expression is 56.

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