2.03 Multiplying and dividing surds
Are the following statements true or false?
\sqrt{8^{2}} = \left(\sqrt{8}\right)^{2}
\sqrt{5^{2}} = \left(\sqrt{5\times 5}\right)^{2}
\sqrt{2^{2}} = \sqrt{2+2}
\sqrt{8^{2}} = \sqrt{16}\times \sqrt{4}
Complete the following statements by following the example:
\sqrt{ 9 \times 4} = \sqrt{9} \times \sqrt{4}=3 \times 2 = 6\sqrt{ 36 \times 25}=\sqrt{⬚} \times \sqrt{⬚}=⬚ \times ⬚ = ⬚
\sqrt{ 9 \times 11} = \sqrt{⬚} \times \sqrt{⬚}=⬚ \sqrt{⬚}
\sqrt{ 49 \times 5} = \sqrt{⬚} \times \sqrt{⬚} = ⬚ \sqrt{⬚}
\sqrt{ 64 \times 3} = \sqrt{⬚} \times \sqrt{⬚} = ⬚ \sqrt{⬚}
Simplify the following:
\sqrt{19} \times \sqrt{17}
\left( 6 \sqrt{8}\right)^{2}
(6 \sqrt{3})^2
Simplify the following:
\sqrt{5} \times \sqrt{7}
8 \times 10 \sqrt{5}
\sqrt{7} \times \sqrt{3} \times \sqrt{11}
\sqrt{55} \times \sqrt{11}
4 \sqrt{11} \times 5
2 \sqrt{5} \times 15 \sqrt{11}
7 \sqrt{22} \times \sqrt{2}
\sqrt{180} \times \sqrt{48}
8 \sqrt{15} \times 8 \sqrt{5}
5 \sqrt{17} \times 8 \sqrt{3}
17 \sqrt{35} \times 4 \sqrt{5}
8 \sqrt{51} \times 9 \sqrt{3}
Simplify the following:
\sqrt{11} \left(\sqrt{7} + 4\right)
\sqrt{7} \left(3 + \sqrt{3}\right)
\sqrt{2} \left(\sqrt{11}-6\right)
3 \sqrt{3} \left(\sqrt{13} - 5\right)
\sqrt{3} \left(\sqrt{11} + \sqrt{13}\right)
4 \sqrt{7} \left(\sqrt{2}-\sqrt{11} \right)
3 \sqrt{5} \left(\sqrt{55} + \sqrt{11}\right)
8 \sqrt{2} \left(\sqrt{3}- 3 \sqrt{7}\right)
5 \sqrt{2} \left( 3 \sqrt{5} + 4 \sqrt{7}\right)
7 \sqrt{3} \left( \sqrt{15} + \sqrt{60}\right)
11 \sqrt{3} \left( 3 \sqrt{5} - \sqrt{20}\right)
8 \sqrt{11} \left( 3 \sqrt{7} - 4 \sqrt{5}\right)
Simplify the following:
\sqrt{2} \left( x \sqrt{2} + 5\right)
4\sqrt{3} \left( x\sqrt{3} + \sqrt{6}\right)
\sqrt{x} \left( 3 \sqrt{x} - 1\right)
2 \sqrt{y} \left( 3 \sqrt{y} - \sqrt{5}\right)
Simplify the following:
\sqrt{15} \div \sqrt{5}
\sqrt{55} \div \sqrt{5}
\sqrt{51} \div \sqrt{17}
\sqrt{21} \div \sqrt{3}
\sqrt{91} \div \sqrt{7}
40 \sqrt{7} \div 8
10 \sqrt{55} \div \sqrt{11}
15 \sqrt{22} \div \sqrt{11}
4 \sqrt{35} \div 2 \sqrt{5}
\sqrt{27} \div \sqrt{3}
3 \sqrt{20} \div \sqrt{5}
5 \sqrt{8} \div \sqrt{2}
40 \sqrt{96} \div 10 \sqrt{6}
50 \sqrt{24} \div 10 \sqrt{6}
\sqrt{25} \div \sqrt{81}
\sqrt{162} \div \sqrt{8}
Simplify the following:
Simplify the following:
Find the exact area of the following rectangles.
Find the area of the trapezium in simplified surd form:
The body surface area of a person in square metres can be modelled by A = \dfrac{\sqrt{h} \times \sqrt{w}}{60}, where A is the surface area, h is the height of the person in cm, and w is the weight of the person in kg.
Use the model to find the surface area of a person who is 164 cm tall and weighs 63 kg. Leave your answer in exact form.
Hence find the approximate surface area of the person, to the nearest hundredth of a square metre.
Find the exact perpendicular height of a triangle whose area is 40 \sqrt{65} square centimetres and whose base measures 10 \sqrt{13} centimetres.
A rectangle has a side length of 8+\sqrt{5}\operatorname{m} and a width of 2\sqrt{5}\operatorname{m}.
Find the exact area of the rectangle.
State the area of the rectangle to the nearest metre.
Find an approximation for the area of the rectangle by rounding the length and width to the nearest metre before multiplying.
Is there a significant difference between the estimated area found by rounding before and after the area calculation?
Ciera needs to perform each of the following calculations, where x=\sqrt{2}. In her calculations Ciera uses x rounded to one decimal place as an approximation.
Determine how much each of her calculations differ from the exact value. Give your answer to 2 decimal places.
10x
x^2+5
50x-2x^2
\dfrac{200}{x}
Vaughan needs 40 lengths of rope, each 1+2\sqrt{3} metres long. Vaughan rounds the rope length required up to the nearest metre and then multiplies by 40 to obtain an approximate amount to purchase from the hardware store.
Determine how much less Vaughan's estimate would be if he had rounded after multiplying the exact length by 40.