Question

write and simplify an expression for the area of each shape.
a)
width: (7 - sqrt{6})
length: (4 + sqrt{6})

b)
side: (2sqrt{18} - sqrt{27})

Explanation:

Write the area expression for shape a

Using the Simplifying Radicals knowledge point

$$
LATEXBLOCK0
$$

Simplify the side length of shape b

Using the Simplifying Radicals knowledge point

$$
LATEXBLOCK1
$$

Calculate the area of shape b

Using the Simplifying Radicals knowledge point

$$
LATEXBLOCK2
$$

Answer:

Question a

The expression for the area of the rectangle is:

$$(4 + \sqrt{6})(7 - \sqrt{6})$$

The simplified expression is:

$$22 + 3\sqrt{6}$$

Question b

The expression for the area of the square is:

$$(2\sqrt{18} - \sqrt{27})^2$$

The simplified expression is:

$$99 - 36\sqrt{6}$$