Simplify:
(i) √(-16) + 3√(-25) + √(-36) - √(- 625)
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Express the following in exponential form. (i) 625 (ii) 1024 (iv) 507 (v) 360
Correct Answer - (i) `5^(4)` (ii) `2^(10)` (iii) `2^(1)xx5^(4)` (iv) `3xx13^(2)` (v) `2^(3)xx3^(2)xx5^(1)`
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(1) If `5^(n+2)=625 ,f i n d[(n+3)]^(1/3)`: (2) If `(32/243)^n=8/27 ,f i n d((n+0. 4)/1024)^(-n)`
Correct Answer - (i) 5 (ii) 64
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(i) Simplify `(2^(2/3)-2^((-2)/3))(2^(4/3)+1+2^((-4)/3))` (ii) `[(root(6)(7))^(2)+(root(6)(7))^(-2)][(root(6)(7))^(4)-1+(root(6)(7))^(-4)]`
Correct Answer - (i) `15/4` (ii) `50/7`
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Simplify :- (i)`(10)/(4)` (ii)`(200)/(50)` (iii)`(27)/(24)` (iv)`(55)/(22)` (v)`(64)/(16)` (vi)`(8)/(6)`
Correct Answer - (i)`(5)/(2)` (ii) 4 (iii)` (9)/(8)` (iv)` (5)/(2)` (v) 4 (vi)`(4)/(3)`
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Simplify :- (i)`(6)/(sqrt(2))` (ii)`(sqrt(3))/(3)` (iii)`sqrt((3)/(4))` (iv)`(6)/(sqrt(2))` (v)`(sqrt(5))/(10)` (vi)`sqrt((16)/(2))`
Correct Answer - (i)`sqrt(2)` (ii)`(1)/(sqrt(3))` (iii)`(sqrt(3))/(2)` (iv)`3sqrt(2)` (v)`(1)/(2sqrt(5))` (vi)`2sqrt(2)`
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Simplify each of the following and express it in the form a + ib : `{:((i),2(3+4i)+i(5-6i),(ii),(3+sqrt(-16))-(4-sqrt(-9))),((iii),(-5+6i)-(2+i),(iv),
Correct Answer - `{:((i),(12+13i),(ii),(-1+7i),(iii),(-3+5i),(iv),"(11-9i)"),((v),(9+22i),(vi),28,(vii),(18-i),(vii),-7sqrt(3)i):}`
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Simplify : 4√(-4) + 5√(-9) – 3√(-16)
\(4\sqrt{-4}+5\sqrt{-9}-3\sqrt{-16}\) = \(4\sqrt{4\times-1}+5\sqrt{9\times-1}-3\sqrt{16\times-1}\) = 4(2i) + 5(3i) - 3(4i) = 8i + 15i - 12i = 11i
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Simplify: (3x+2)(9x^2-6xy+4y^2)
a3−b3=(a−b)(a2+ab+b2) a3+b3=(a+b)(a2−ab+b2) Given, (3x+2y)(9x2−6xy+4y2) =(3x)3+(2y)3 =27x3+8y3
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39) Simplify: \( \frac{a^{2}-16}{a^{3}-8} \times \frac{2 a^{2}-3 a-2}{2 a^{2}+9 a+4} \div \frac{3 a^{2}-11 a-4}{a^{2}+2 a+4} \)
\(\frac{a^2+6}{a^3-8}\) x \(\frac{2a^2-3a-2}{2a^2+9a+4}\) ÷ \(\frac{3a^2-11a-4}{a^2+2a+4}\) = \(\frac{(a+4)(a-4)}{(a-2)(a^2+2a+4)}\) x \(\frac{(2a+1)(a-2)}{(2a+1)(a+4)}\) x \(\frac{(a+2)^2}{(3a+1)(a-4)}\) = \(\frac{(a+2)^2}{(a^2+2a+4)(3a+1)}\)
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