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Class 10MathematicsReal NumbersIrrational numbersHardLevel 15
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If (a=5+\sqrt{7}) and (b=5-\sqrt{7}), what is the value of (ab)?

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Answer and explanation

Correct answer: (18)

Step 1: This is multiplication of conjugates. Step 2: (ab=5^2-(\sqrt{7})^2=25-7=18). Step 3: In conjugate multiplication, the middle irrational terms cancel.

Related tags

Conjugate SurdsRational ProductClass 10

Frequently asked questions

What is the correct answer to this question?

(18)

Why is this the correct answer?

Step 1: This is multiplication of conjugates. Step 2: (ab=5^2-(\sqrt{7})^2=25-7=18). Step 3: In conjugate multiplication, the middle irrational terms cancel.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Irrational numbers.

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  1. 1Which of the following numbers is irrational?
  2. 2Which of the following numbers is rational?
  3. 3What type of number is (\sqrt{16})?
  4. 4Which statement about (\sqrt{10}) is correct?
  5. 5Which of the following is an example of an irrational number?
  6. 6Which decimal form represents an irrational number?
  7. 7What type of number is (0.3333\ldots)?
  8. 8Which statement is correct about (0.101001000100001\ldots)?
  9. 9If (a) is a non-zero rational number and (b) is an irrational number, what type of number is (ab) generally?
  10. 10What type of number is (\sqrt{2}+3)?
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