Robert Bosch Surds and Indices Quiz 2

Explanation:

(  (-2 )^{{-2 } )^{-2 } = \frac{1}{((-2)^{-2})^{2}}

 

= \frac{1}{(-2)^{-4}} = (-2)^{4} = 16

 

Explanation:

 

(256)^{0.16} \times (4)^{0.36}

= (44)^{0.16} \times 4^{0.36} = 4^{0.64} \times 4^{0.36}

= (4)^{0.64 + 0.36} = 4

Explanation:

((-\frac{1}{2})^{2})^{-2 \times (-1)}) 

= (-\frac{1}{2})^{2\times 2}

= (-\frac{1}{2})^{4} = 16

Explanation:

= \frac{0.3555 \times 0.5555 \times 2.025}{0.225 \times 1.7775 \times 0.2222 }

= \frac{3555 \times 5555\times 2025}{225 \times 17775\times 2222 }

=4. 5 

 

Explanation:

(6.5 \times 6.5 – 45.5 + 3.5 \times 3.5)

= [(6.5)^{2} – 2 \times 6.5 \times 3.5 + (3.5)^{2}]

= (6.5 – 3.5)^{2}= (3)^{2}

 = 9

Explanation:

= (7.5\times7.5 + 37.5 + 2.5 \times2.5)

= [(7.5)^{2} + 2 \times 7.5 \times× 2.5 + (2.5)^{2}]

= [7.5 + 2.5]^{2}

 = (10)^{2}

 = 100

Explanation:

 Let, 1.49 = a and 0.51 = b 

\therefore  \frac{a^{2} - b^{2}}{a-b}

 = \frac{(a+b)(a-b)}{ (a-b)}= a + b

= 1.49 + 0.51 = 2

 

Explanation:

Let 0.796 = a and 0.204 = b 

\ Expression = \frac{axa-bxb}{a- b }

= \frac{a^{2} - b^{2}}{a-b}

 = \frac{(a+b)(a-b)}{ (a-b)}

 = a + b 

= 0.796 + 0.204 = 1

Explanation:

Expression = 0.75 \times 7.5 – 2\times  7.5 \times 0.25 + 0.25 \times 2.5

 = 0.75 \times 0.75 \times 10 –2 \times 0.75 \times 0.25 \times10 + 0.25\times0.25\times10

= 10 ((0.75)^{ 2} - 2 \times 0.75 \timesx 0.25 +(0.25)^{2})

=10(0.75–0.25)^{2} = 10 \times 0.25 = 2.5

Explanation:

Expression = (8.7 + 1.3)^{2}

[a^{ 2} + 2ab + b^{ 2}= (a + b)^{ 2} ]

= 10^{2} = 100