1.09 Binomial expansions with surds
Expand the following brackets:
\left(5 - \sqrt{13}\right) \left(5 + \sqrt{13}\right)
\left(\sqrt{11} - 11\right) \left(\sqrt{11} + 11\right)
\left( 8 \sqrt{5} - 6\right) \left( 8 \sqrt{5} + 6\right)
\left(\sqrt{7} + \sqrt{5}\right) \left(\sqrt{7} - \sqrt{5}\right)
\left( 7 \sqrt{11} - \sqrt{7}\right) \left( 7 \sqrt{11} + \sqrt{7}\right)
\left( 5 \sqrt{3} + 3 \sqrt{5}\right) \left( 5 \sqrt{3} - 3 \sqrt{5}\right)
Expand the following brackets:
\left(\sqrt{3} - 13\right)^{2}
\left(\sqrt{7} + \sqrt{3}\right)^{2}
\left( 3 \sqrt{3} + 8\right)^{2}
\left( 4 \sqrt{2} - \sqrt{13}\right)^{2}
\left( 3 \sqrt{2} + 4 \sqrt{13}\right)^{2}
\left(5 \sqrt{2} - \sqrt{32} \right)^{2}
Expand the following brackets:
\left(\sqrt{11} + 10\right) \left(\sqrt{3} - 9\right)
\left(\sqrt{11} - \sqrt{13}\right) \left(\sqrt{7} - \sqrt{2}\right)
\left( 11 \sqrt{2} - \sqrt{7}\right) \left( 13 \sqrt{3} - \sqrt{5}\right)
\left( 4 \sqrt{2} - \sqrt{7}\right) \left( 3 \sqrt{3} + \sqrt{8}\right)
\left( 17 \sqrt{3} - 8\sqrt{8}\right) \left(\sqrt{24} - \sqrt{5}\right)
\left( \sqrt{90} - 7\sqrt{7}\right) \left(\sqrt{72} - 6\sqrt{5}\right)
Consider the following equation:
\left( 3 \sqrt{35} - 2 \sqrt{7}\right)^{2} = x - y \sqrt{5}
Expand and simplify the left hand side of the equation.
State the values of x and y.
Consider the following equation:
\left(\sqrt{m} + n\right)^{2} = 16 + 6 \sqrt{7}
Expand and simplify the left hand side of the equation.
State the values of m and n.
Consider the following expression:
\left(\sqrt{a} + 7\right)^{2} = 54+b \sqrt{5}
Expand and simplify the left hand side of the equation.
State the values of a and b.
Consider the following expression:
\left(x\sqrt{y} + 5\right)^{2} = 33+ 4\sqrt{2}
Expand and simplify the left habd side of the equation.
State the values of x and y.
Consider the following expression:
\left(\sqrt{7} + 4\right)^{2} + \left(\sqrt{7} + m\right)^{2}
Expand and simplify the expression.
Hence what value of m can be substituted into \left(\sqrt{7} + 4\right)^{2} + \left(\sqrt{7} + m\right)^{2} so that it has a rational value?
Consider the following right triangle:
Find c, the length of the hypotenuse of the triangle.
Find the exact perimeter of the figure.
Find the exact area of the figure.
Consider the following isosceles triangle:
Find h, the height of the isosceles triangle.
Find the exact perimeter of the triangle.
Find the exact area of the triangle.
