The distributive law with surds | Maths | Quizalize & Oak National Academy

Starter quiz

Simplify the expression $\sqrt {24a^{2}b} \times \sqrt {3a^{2}b}$

$2a\sqrt {6b} \times a\sqrt {3b}$

$6a^{2}b\sqrt {2}$ ✓

$2a^{2}\sqrt {18b^{2}}$

$18a^{2}b\sqrt {2}$
Simplify the expression $\sqrt {24 \over 30} \times \sqrt {5 \over 25}$

'0.4' ✓
$\sqrt {28} \times \sqrt {80} = w\sqrt {b}$ . Write down the value of $b$ .

'35' ✓
$\sqrt {28} \times \sqrt {80} = w\sqrt {b}$ . Write down the value of $w$ .

'8' ✓
Simplify the expression: $\sqrt {12} + \sqrt {27} - \sqrt {48}$

$-3\sqrt {3}$

$4\sqrt {3} + 9\sqrt {3} - 16\sqrt {3}$

$\sqrt {3}$ ✓

$2\sqrt {3} + 3\sqrt {3} - 4\sqrt {3}$
Simplify the expression: $\sqrt {75} - \sqrt {27} + \sqrt {48}$

$6\sqrt {3}$ ✓

$5\sqrt {3} - 3\sqrt {3} + 4\sqrt {3}$

$32\sqrt {3}$

$25\sqrt {3} - 9\sqrt {3} + 16\sqrt {3}$

Match the statements with the equations that demonstrate each law.

The distributive law

⇔

$a(b+c) = ab + ac$ ✓

The associative law

⇔

$(a+b) + c = a + (b + c)$ ✓

The commutative law

⇔

$a+b = b+a$ ✓
Expand $4(3\sqrt {5} + \sqrt {27})$

$12\sqrt {5} + 4\sqrt {3}$

$12\sqrt {5} + 12\sqrt {3}$ ✓

$12\sqrt {5} + 3\sqrt {3}$

$12\sqrt {5} + 4\sqrt {27}$
Write $\sqrt {3}(\sqrt {8} + \sqrt {20})$ in the form $a\sqrt {b} + c\sqrt {d}$ . What is the value of $a$ ?

2 ✓

4

6

15
Write $\sqrt {3}(\sqrt {8} + \sqrt {20})$ in the form $a\sqrt {b} + c\sqrt {d}$ , where $b>d$ . What is the value of $b$ ?

2

4

6

15 ✓
Write $\sqrt {3}(\sqrt {8} + \sqrt {20})$ in the form $a\sqrt {b} + c\sqrt {d}$ . What is the value of $c$ ?

2 ✓

4

6

15
Write $\sqrt {3}(\sqrt {8} + \sqrt {20})$ in the form $a\sqrt {b} + c\sqrt {d}$ , where $b>d$ . What is the value of $d$ ?

2

4

6 ✓

15

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Knowing how to perform arithmetic operations with surds means the distributive law can be considered.
Surds could be seen in either the term or the binomial.

Pupils may struggle with applying the distributive law to expressions involving surds.

The area model can be used here to demonstrate how terms are multiplied when expanding the bracket.

Distributive law - The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.