Applying the underlying structure of multiplication and division of surds

Maths

In the prior unit, pupils explored the concept of square root, including calculating this on their calculators. In this unit, pupils work with surds and the notion that a surd is both an operation and the result of that operation.

Surds

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

Simplify the expression $$\sqrt {3 \over 4} \times \sqrt {1 \over 3}$$

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

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

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

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

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

Calculate $${9 \over \sqrt {3}} \times {9 \over \sqrt {3}}$$

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

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

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

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

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