b: B=căn 49a^2+3a

=|7a|+3a

=7a+3a(a>=0)

=10a

c: C=căn16a^4+6a^2

=4a^2+6a^2

=10a^2

d: \(D=3\cdot3\cdot\sqrt{a^6}-6a^3=6\cdot\left|a^3\right|-6a^3\)

TH1: a>=0

D=6a^3-6a^3=0

TH2: a<0

D=-6a^3-6a^3=-12a^3

e: \(E=3\sqrt{9a^6}-6a^3\)

\(=3\cdot\sqrt{\left(3a^3\right)^2}-6a^3\)

=3*3a^3-6a^3(a>=0)

=3a^3

f: \(F=\sqrt{16a^{10}}+6a^5\)

\(=\sqrt{\left(4a^5\right)^2}+6a^5\)

=-4a^5+6a^5(a<=0)

=2a^5

a) \(5\sqrt{25a^2}-25=25\left|a\right|-25==-25a-25\left(a< 0\right)\)

b) \(\sqrt{49a^2}+3a=7\left|a\right|+3a=-7a+3a\left(a< 0\right)=-4a\)

c) \(3\sqrt{9a^6}=9\left|a^3\right|-6a^3\)

Xét \(a\ge0\Rightarrow9\left|a^3\right|-6a^3=9a^3-6a^3=3a^3\)

Xét \(a< 0\Rightarrow9\left|a^3\right|-6a^3=-9a^3-6a^3=-15a^3\)

a) 5\(\sqrt{25a^2}\) - 25 với a < 0

= 5\(\sqrt{\left(5a\right)^2}\) - 25

= 5.\(\left|5a\right|\) - 25

= 5.-(5a) - 25 

= -25a - 25 Vì a < 0

b) \(\sqrt{49a^2}\) + 3a với a < 0

= \(\sqrt{\left(7a\right)^2}\) + 3a

= \(\left|7a\right|\) + 3a

= -7a + 3a Vì a < 0

= -4a

c) 3\(\sqrt{9a^6}\) - 6a³ với a bất kì

= 3\(\sqrt{\left(3a^3\right)^2}\) - 6a³

= 3\(\left|3a^3\right|\) - 6a³

= 9a³ - 6a³

= 3a³

 Chúc bạn học tốt

a) \(5\sqrt{25a^2}-25=-25a-25\)

b) \(\sqrt{49a^2}+3a=-7a+3a=-4a\)

c) \(3\sqrt{9a^6}-6a^3=6a^3-6a^3=0\)

Lời giải:

a)

$5\sqrt{25a^2}-25a=5\sqrt{(5a)^2}-25a=5|5a|-25a$

Với $a\leq 0$ thì $|5a|=-5a$. Do đó:

$5\sqrt{25a^2}-25a=-25a-25a=-50a$

b)

$\sqrt{16a^4}+6a^2=\sqrt{(4a^2)^2}+6a^2=|4a^2|+6a^2=4a^2+6a^2=10a^2$

a) \(=5\left|a\right|+3a=5a+3a=8a\)

b) \(=3\left|a^2\right|+3a^2=3a^2+3a^2=6a^2\)

c) \(=5.2\left|a^3\right|-3a^3=-10a^3-3a^3=-13a^3\)

\(P=\dfrac{9\sqrt{a}-\sqrt{25a}+\sqrt{4a^3}}{a^2+2a}=\dfrac{9\sqrt{a}-5\sqrt{a}+2a\sqrt{a}}{a\left(a+2\right)}=\dfrac{4\sqrt{a}+2a\sqrt{a}}{a\left(a+2\right)}=\dfrac{2\sqrt{a}\left(2+a\right)}{a\left(2+a\right)}=\dfrac{2\sqrt{a}}{a}=\dfrac{2.\sqrt{a}}{\sqrt{a}.\sqrt{a}}=\dfrac{2}{\sqrt{a}}\)