Step-by-step explanation:

SIMPLIFY \sqrt{28}

28

to 2\sqrt{7}2

7

.

2\sqrt{7}\sqrt{18}\times \frac{\sqrt{75}}{\sqrt{27}}\sqrt{15}\sqrt{42}

2

7

18

×

27

75

15

42

2 Simplify \sqrt{18}

18

to 3\sqrt{2}3

2

.

2\sqrt{7}\times 3\sqrt{2}\times \frac{\sqrt{75}}{\sqrt{27}}\sqrt{15}\sqrt{42}

2

7

×3

2

×

27

75

15

42

3 Simplify \sqrt{75}

75

to 5\sqrt{3}5

3

.

2\sqrt{7}\times 3\sqrt{2}\times \frac{5\sqrt{3}}{\sqrt{27}}\sqrt{15}\sqrt{42}

2

7

×3

2

×

27

5

3

15

42

4 Simplify \sqrt{27}

27

to 3\sqrt{3}3

3

.

2\sqrt{7}\times 3\sqrt{2}\times \frac{5\sqrt{3}}{3\sqrt{3}}\sqrt{15}\sqrt{42}

2

7

×3

2

×

3

3

5

3

15

42

5 Cancel \sqrt{3}

3

.

2\sqrt{7}\times 3\sqrt{2}\times \frac{5}{3}\sqrt{15}\sqrt{42}

2

7

×3

2

×

3

5

15

42

6 Cancel 33.

2\sqrt{7}\sqrt{2}\times 5\sqrt{15}\sqrt{42}

2

7

2

×5

15

42

7 Simplify.

2\times 5\sqrt{7\times 2\times 15\times 42}

2×5

7×2×15×42

8 Simplify 7\times 27×2 to 1414.

2\times 5\sqrt{14\times 15\times 42}

2×5

14×15×42

9 Simplify 14\times 1514×15 to 210210.

2\times 5\sqrt{210\times 42}

2×5

210×42

10 Simplify 210\times 42210×42 to 88208820.

2\times 5\sqrt{8820}

2×5

8820

11 Simplify \sqrt{8820}

8820

to 42\sqrt{5}42

5

.

2\times 5\times 42\sqrt{5}

2×5×42

5

12 Simplify.

420\sqrt{5}

420

5