Robert Bosch Surds and Indices Quiz 3

Explanation:

(0.98)^{3} + (0.02)^{3} + 3 \times0.98 \times 0.2 – 1

 = 0.941192 + 0.000008+0.0588– 1

= 1 – 1 = 0 

Explanation:

 

Expression =   0.65\times0.65 + 0.35\times 0.35 + 2\times0.35\times0.65

= (0.65 + 0.35)^{2}

 = (1)^{2}= 1

Explanation:

\frac{2.4 \times 10^{3}}{8  \times 10^{-2}}

=\frac{24 \times10^{3}}{8 \times 10 \times 10^{-2}} 

=\frac{24 \times 10^{3} = 3 \times 10^{4}

 

Explanation:

 

[3– 4(3 – 4)^{–1}]^{ –1}

[3– 4(-1)^{–1}]^{ –1}

[\frac{(3-4)}{{–1}}]^{ –1}

= [3 + 4]^{-1}

= (7)^{-1} = 1/7

Explanation:

 a = 55, b = 17, c = – 72 

a + b + c = 55 + 17 – 72 = 0 

\therefore a^{3}  + b^{3} + c^{3}– 3abc = 0

Explanation:

= (0.2)^{3} \times 200 +2000 of (0.2)^{2}

= (0.2)^{3} \times 200 + (2000 \times 0.2 \times 0.2)

=  \frac{0. 2 \times  0. 2 \times 0. 2\times 200}{2000\times 2\times2 \times 10 }

= 2/100

= 1/50

Explanation:

= \frac{(75.8)^{2}-( 35. 8)^{2}}{40}

= \frac{(75.8+ 35. 8)(75.8- 35.8)}{40}

= 111.6 * \frac{40}{40}

= 111.6

Explanation:

1^{ 3} + 2^{ 3} + ..... + 10^{ 3} = 3025

\therefore  2^{ 3} + 4^{ 3} + ...... + 20^{ 3}

= 2^{ 3} (1 + 2^{ 3} + ...... + 10^{ 3} )

= 8 * 3025 = 24200

Explanation:

(d^{ s + t} ÷ d^{ s} ) ÷ d^{ t}

= d ^{s + t – s} ÷ d ^{t}

= d ^{t}  ÷  d ^{t}  = 1

Explanation:

(2^{51} + 2^{52} + 2^{53} + 2^{54} + 2^{55})

= 2^{51} (1 + 2 + 22 + 23 + 24 )

 = 2^{51} (1 + 2 + 4 + 8 + 16)

= 2^{51}\times 31

= 2^{49} \times 4 \times31

= 2^{49}\times 124