Simplifying surds questions with answers

Questions

1. Question 1Simplify one surd

   Simplify $\sqrt{175}$.

   Show the worked solution

   1. Step 1: Write 175 as the biggest square number times another number$175 = 25 \times 7$
   2. Step 2: √(a × b) = √a × √b: the square number comes out as its square root$\sqrt{175} = 5\sqrt{7}$
2. Question 2Simplify one surd

   Simplify $\sqrt{180}$.

   Show the worked solution

   1. Step 1: Write 180 as the biggest square number times another number$180 = 36 \times 5$
   2. Step 2: √(a × b) = √a × √b: the square number comes out as its square root$\sqrt{180} = 6\sqrt{5}$
3. Question 3Add or subtract like surds

   Simplify $\sqrt{18} - \sqrt{8}$, giving your answer in the form $a\sqrt{b}$.

   Show the worked solution

   1. Step 1: Simplify each surd: take out the biggest square factor, keeping the number in front$\sqrt{18} = 3\sqrt{2}$$-\sqrt{8} = -2\sqrt{2}$
   2. Step 2: They are now like surds: collect them$3\sqrt{2} - 2\sqrt{2} = \sqrt{2}$
4. Question 4Add or subtract like surds

   Simplify $\sqrt{12} - \sqrt{75}$, giving your answer in the form $a\sqrt{b}$.

   Show the worked solution

   1. Step 1: Simplify each surd: take out the biggest square factor, keeping the number in front$\sqrt{12} = 2\sqrt{3}$$-\sqrt{75} = -5\sqrt{3}$
   2. Step 2: They are now like surds: collect them$2\sqrt{3} - 5\sqrt{3} = -3\sqrt{3}$
5. Question 5Three surds

   Simplify $\sqrt{48} - \sqrt{3} + 2\sqrt{27}$, giving your answer in the form $a\sqrt{b}$.

   Show the worked solution

   1. Step 1: Simplify each surd: take out the biggest square factor, keeping the number in front$\sqrt{48} = 4\sqrt{3}$$-\sqrt{3}$ is already in simplest form$2\sqrt{27} = 2 \times 3\sqrt{3}$$= 6\sqrt{3}$
   2. Step 2: They are now like surds: collect them$4\sqrt{3} - \sqrt{3} + 6\sqrt{3} = 9\sqrt{3}$
6. Question 6Three surds

   Simplify $\sqrt{27} - \sqrt{12} + 2\sqrt{48}$, giving your answer in the form $a\sqrt{b}$.

   Show the worked solution

   1. Step 1: Simplify each surd: take out the biggest square factor, keeping the number in front$\sqrt{27} = 3\sqrt{3}$$-\sqrt{12} = -2\sqrt{3}$$2\sqrt{48} = 2 \times 4\sqrt{3}$$= 8\sqrt{3}$
   2. Step 2: They are now like surds: collect them$3\sqrt{3} - 2\sqrt{3} + 8\sqrt{3} = 9\sqrt{3}$