Applying the underlying structure of multiplication and division of surds | Maths

Starter quiz

Calculate $\sqrt {0.764} \times \sqrt {0.764}$

'0.764' ✓
Calculate ${9 \over \sqrt {3}} \times {9 \over \sqrt {3}}$

'27' ✓
$2\sqrt {5} \times \sqrt {2} = 2\sqrt {b}$ . What is the value of $b$ ?

'10' ✓
$\sqrt {6} \times \sqrt {4} \times 3\sqrt {10}\times \sqrt {10} = a\sqrt {6}$ . What is the value of $a$ ?

'60' ✓
Simplify the following expression: $\sqrt {24} \div \sqrt {6}$

'2' ✓
Evaluate the following expression: $3\sqrt {20} \div \sqrt {5}$

'6' ✓

Simplify the expression $\sqrt {4ab} \times \sqrt {7a^{2}b}$

$2\sqrt {ab} \times \sqrt {7a^{2}b}$

$2\sqrt {ab} \times a\sqrt {7ab}$

$\sqrt {28a^{3}b^{2}}$

$2ab\sqrt {7a}$ ✓
Simplify the expression $\sqrt {3 \over 4} \times \sqrt {1 \over 3}$

$1 \over 2$ ✓

$\sqrt {3 \over 12}$

$1 \over 4$

$\sqrt {1 \over 4}$
Simplify the expression: $\sqrt {12} \times \sqrt {27}$

$\sqrt {324}$

18 ✓

$2\sqrt {3} \times 3\sqrt {3}$

54
Simplify $\sqrt {48} \times \sqrt {12}$

'24' ✓
Calculate $(2\sqrt {48} - 5\sqrt {48}) \times \sqrt {12}$

'-72' ✓
Complete the rule for dividing surds: $\sqrt {x \over y} =$

$\sqrt {x} \over y$

$x \over \sqrt {y}$

$\sqrt {x} \over \sqrt {y}$ ✓

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Pupils may insist that a square root can be both positive and negative.

By convention, square root refers to the principal (positive) square root.

Surd - A surd is an irrational number expressed as the root of a rational number.
Radical - The root sign is the radical symbol.
Radicand - The radicand is the value inside the radical symbol.