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Find the square of : sqrt(3)+ sqrt(2)...

Find the square of :
`sqrt(3)+ sqrt(2)`

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To find the square of \( \sqrt{3} + \sqrt{2} \), we can follow these steps: ### Step 1: Write the expression We start with the expression we need to square: \[ (\sqrt{3} + \sqrt{2})^2 \] ### Step 2: Use the identity for squaring a binomial We can use the algebraic identity for squaring a binomial, which states: \[ (a + b)^2 = a^2 + b^2 + 2ab \] In our case, let \( a = \sqrt{3} \) and \( b = \sqrt{2} \). ### Step 3: Calculate \( a^2 \) and \( b^2 \) Now we calculate \( a^2 \) and \( b^2 \): \[ a^2 = (\sqrt{3})^2 = 3 \] \[ b^2 = (\sqrt{2})^2 = 2 \] ### Step 4: Calculate \( 2ab \) Next, we calculate \( 2ab \): \[ 2ab = 2 \times \sqrt{3} \times \sqrt{2} = 2 \times \sqrt{6} \] ### Step 5: Combine all parts Now we can combine all the parts together: \[ (\sqrt{3} + \sqrt{2})^2 = a^2 + b^2 + 2ab = 3 + 2 + 2\sqrt{6} \] \[ = 5 + 2\sqrt{6} \] ### Final Answer Thus, the square of \( \sqrt{3} + \sqrt{2} \) is: \[ \boxed{5 + 2\sqrt{6}} \]
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ICSE-RATIONAL AND IRRATIONAL NUMBERS -EXERCISE 1 (B)
  1. State, whether the following numbers are rational or not: ((sqrt(7))...

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  2. Find the square of : (3sqrt(5))/(5)

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  3. Find the square of : sqrt(3)+ sqrt(2)

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  4. Find the square of : sqrt(5)-2

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  5. Find the square of : 3+2sqrt(5)

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  6. State in each case whether true or false: sqrt(2) + sqrt(3)= sqrt(5...

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  7. State in each case whether true or false: 2sqrt(4)+2=6

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  8. State in each case whether true or false: 3sqrt(7)-2sqrt(7)= sqrt(7...

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  9. State in each case whether true or false: (2)/(7) is an irrational n...

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  10. State in each case whether true or false: (5)/(11) is a rational num...

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  11. State in each case whether true or false: All rational numbers are r...

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  12. State in each case whether true or false: All real numbers are ratio...

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  13. State in each case whether true or false: Some real numbers are rat...

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  14. Given universal set = { -6 , -5 (3)/(4) , -sqrt(4), - (3)/(5), -(3)/(8...

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  15. Prove that each of the numbers is irrational : sqrt(3) +sqrt(2)

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  16. Prove that each of the numbers is irrational : 3-sqrt(2)

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  17. Prove that each of the numbers is irrational : sqrt(5) -2

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  18. Write a pair of irrational numbers whose sum is irrational .

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  19. Write a pair of irrational numbers whose sum is rational .

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  20. Write of pair of irrational numbers whose difference is irrational .

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