Question

operation on real numbers​

Answer 1

Answer:

Operations On Real Numbers. ... When the addition or subtraction operation is done on a rational and an irrational number, the result is an irrational number. When the multiplication or division operation is done on a rational number with an irrational number, the result is an irrational number.

Step-by-step explanation:

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Answer 2

Answer:

When the addition or subtraction operation is done on a rational and an irrational number, the result is an irrational number.

When the multiplication or division operation is done on a rational number with an irrational number, the result is an irrational number.

When two irrational numbers are added, subtracted, multiplied or divided, the result may be a rational or an irrational number.

If a and b are positive real numbers, then we have,

√ab = √a √b

Real Numbers

(√a + √b)(√a – √b) = a – b

(a + √b)(a – √b) = a2 – b

(√a + √b)(√c + √d) = √ac + √ad + √bc + √bd

(√a + √b)2 = a + 2√ab + b

Examples

Solve (2√2 + 7√7) + (13√2 – 4√7).

Solution:

(2√2 + 7√7) + (13√2 – 4√7)

= (2√2 + 13√2) + (7√7 – 4√7)

= (2 + 13)√2 + (7-4)√7

= 15√2 + 3√7

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