1.08 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{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:
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.